Unit 3 Electromagnetism. Class Questions

Transcription

1 Unit 3 Electromagnetism Class Questions

2 Contents TUTORIAL 1 TUTORIAL 2 TUTORIAL 3 Coulomb's Inverse Square Law Electric Field Strength Electrostatic Potential PAST PAPERS 2012 Q5, 2011 Q5, 2010 Q6, 2009 Q4, 2008 Q5, 2008 Q8, 2007 Q5, 2006 Q5, TUTORIAL 4 Charges in Motion PAST PAPERS 2010 Q8, 2006 Q6, TUTORIAL 5 TUTORIAL 6 Force on a Conductor Charged Particles in Magnetic Fields PAST PAPERS 2006 Q7, 2007 Q6, 2007 Q8, 2009 Q5, 2010 Q7, 2011 Q7, 2011 Q8, 2012 Q6, 2012 Q8 TUTORIAL 7 Self Inductance PAST PAPERS 2006 Q8, 2007 Q7, 2008 Q7, 2009 Q6, 2011 Q6, 2012 Q7 TUTORIAL 8 PAST PAPERS PAST PAPERS Forces of Nature 2006 Q9, 2009 Q4 Capacitors in a d.c. circuit CSYS 1994 Q6, CSYS 1995 Q12 (d), CSYS 1998 Q6 Inductive Reactance CSYS 1995 Q15, CSYS 1997 Q15(a), CSYS 1999 Q14, CSYS 2000 Q14 (e) Electron Volt Ferromagnetism 2

3 TUTORIAL 1 Coulomb's Inverse Square Law Q1 A charge of x 10-8 C is placed a distance of 2.0 mm from a charge of -4.0 x 10-8 C. (a) Calculate the electrostatic force between the charges. (b) The distance between the same charges is adjusted until the force between the charges is 1.0 x 10-4 N. Calculate this new distance between the charges. Q2 Q3 Q4 Compare the electrostatic and gravitational forces between a proton and electron which have an average separation of 2.0 x m. Use G = 6.67 x N m 2 kg -2. Let us imagine the Earth (mass 6.0 x kg) suddenly has an excess of positive charge and the Moon (mass 7.3 x kg) suddenly has an equal excess of positive charge. Calculate the size of the charge required so that the electrostatic force balances the gravitational force. The diagram below shows three charges fixed in the positions shown. Q1 = x 10-6 C, Q2 = x 10-6 C and Q3 = x 10-6 C. Calculate the resultant force on charge Q1. (Remember that this resultant force will have a direction as well as magnitude). Q5 Two like charged spheres of mass 0.10 g, hung from the same point by silk threads are repelled from each other to a separation of 1.0 cm by the electrostatic force. The angle between one of the silk threads and the vertical is 5.7. (a) By drawing a force diagram, find the electrostatic force F E between the spheres. (b) Calculate the size of the charge on each sphere. (c) The average leakage current from a charged sphere is 1.0 x A. How long would it take for the spheres to discharge completely?

4 (d) Describe how the two spheres may be given identical charges. Q6 In an experiment to show Coulomb's Law, an insulated, light, charged sphere is brought close to another similarly charged sphere which is suspended at the end of a thread of length 0.80 m. The mass of the suspended sphere is 0.50 g. It is found that the suspended sphere is displaced to the left by a distance of 16 mm as shown below. (a) Make a sketch showing all of the forces acting on the suspended sphere. (b) Calculate the electrostatic force acting on the suspended sphere. Q7. Explain how a charged strip of plastic can pick up small pieces of paper even although the paper has no net charge. TUTORIAL 2 Electric Field Strength Q1 What is the electric field strength at a point where a small object carrying a charge of 4.0 μc experiences a force of 0.02 N? Q2 (a) Calculate the size of a point charge required to give an electric field strength of 1.0 N C -1 at a distance of 1.0 m from the point charge. (b) State the magnitude of the electric field strength at a distance of 2.0m from the point charge. 4

5 Q3 (a) Calculate the electric field strength due to an α-particle at a point 5.0mm from the α-particle. (b) How would the electric field strength calculated in (a) compare with the electric field strength at a point 5.0 mm from a proton? Q4 The diagram below shows two charges of nc and nc respectively separated by 0.13m. (a) Calculate the magnitude of the resultant electric field strength at the point P as shown in the diagram above. (b) Make a sketch like the one above and show the direction of the resultant electric field strength at the point P. Angles are required on your sketch. Q5 A negatively charged sphere, of mass 2.0 x 10-5 kg, is held stationary in the space between two charged metal plates as shown in the diagram below. (a) The sphere carries a charge of x 10-9 C. Calculate the size of the electric field strength in the region between the metal plates. (b) Make a sketch of the two plates and the stationary charged sphere. Show the shape and direction of the resultant electric field in the region between the plates.

6 Q6 Two charges of +8.0 x 10-9 C and +4.0 x 10-9 C are held a distance of 0.20m apart. (a) Calculate the magnitude and direction of the electric field strength at the midpoint between the charges. (b) Calculate the distance from the 8.0 x 10-9 C charge at which the electric field strength is zero. (c) The 4.0 x 10-9 C charge has a mass of 5.0 x 10-4 kg. (i) (ii) Calculate the magnitude of the electrostatic force acting on the charge. Calculate the magnitude of the gravitational force acting on the mass. Q7 Copy and complete the electric field patterns for: (a) the electric field between two parallel plates which have equal but opposite charges (b) the electric field around 2 unequal but opposite charges. Q8 Draw electric field lines and equipotential surfaces for the two oppositely charged parallel plates shown in the sketch below. (Include the fringing effect usually observed near the edge of the plates). 6

7 TUTORIAL 3 Electrostatic Potential Q1 Calculate the electrostatic potential at a point, P, which is at a distance of 0.05 m from a point charge of x 10-9 C. Q2 Small spherical charges of +2.0 nc, -2.0 nc, +3.0 nc and +6.0 nc are placed in order at the corners of a square of diagonal 0.20 m as shown in the diagram below. (a) Calculate the electrostatic potential at the centre, C, of the square. (b) D is at the midpoint of the side as shown. Calculate the electrostatic potential difference between point C and point D. Q3 A hydrogen atom may be considered as a charge of x C separated from a charge of -1.6 x C by a distance of 5.0 x m. Calculate the potential energy associated with an electron in a hydrogen atom. Q4 Consider an equilateral triangle PQR where QR = 20 mm. A charge of +1.0 x 10-8 C is placed at Q and a charge of -1.0 x 10-8 C is placed at R. Both charges are fixed in place. (a) Calculate the electric field strength at point P. (b) Calculate the electrostatic potential at point P. Q5 The diagram below shows two horizontal metal plates X and Y which are separated by a distance of 50 mm.. There is a potential difference between the plates of 1200 V. Note that the lower plate, X, is earthed.

8 (a) Draw a sketch graph to show how the potential varies along a line joining the mid-point of plate X to the mid-point of plate Y. (b) Calculate the electric field strength between the plates. (c) Explain how the value for the electric field strength can be obtained from the graph obtained in (a). Q6 (a) State what is meant by an equipotential surface. (b) The sketch below shows the outline of the positively charged dome of a Van de Graaff generator. Copy this sketch and show the electric field lines and equipotential surfaces around the charged dome. Q7 Two oppositely charged parallel plates have a potential difference of 1500 V between them. If the plates are separated by a distance of 20 mm calculate the electric field strength, in V m -1, between the plates. Q8 A uniform electric field is set up between two oppositely charges parallel metal plates by connecting them to a 2000 V d.c. supply. The plates are 0.15 m apart. (a) Calculate the electric field strength between the plates. 8

9 (b) An electron is released from the negative plate. (i) (ii) (iii) State the energy change which takes place as the electron moves from the negative to the positive plate. Calculate the work done on the electron by the electric field. Using your answer to (ii) above calculate the velocity of the electron as it reaches the positive plate. Q9 A proton is now used in the same electric field as question 8 above. The proton is released from the positive plate. (a) Describe the motion of the proton as it moves towards the negative plate. (b) (i) Describe how the work done on the proton by the electric field compares with the work done on the electron in question 8. (ii) How does the velocity of the proton just as it reaches the negative plate compare with the velocity of the electron as it reaches the positive plate in the previous question? Q10 (a) A sphere of radius 0.05 m has a potential at its surface of 1000 V. Make a sketch of the first 5 equipotential lines outside the sphere if there is 100 V between the lines. (i.e. calculate the various radii for these potentials). (b) Calculate the charge on the sphere. Q11 (a) Using the equation calculate the speed of an electron which has been accelerated through a potential difference of 1.0 x 10 6 V. (b) Is there anything wrong with your answer?

10 Past paper Questions: 2012 Q5 (a) An uncharged conducting sphere is suspended from a fixed point X by an insulating thread of negligible mass as shown in Figure 5A. A charged plate is then placed close to the sphere as shown below. Explain why the uncharged sphere is attracted to the charged plate. You may use a diagram to help explain your answer. 1 (a) The sphere is now given a negative charge of 140 nc and placed between a pair of parallel plates with a separation of 42 mm as shown below. When a potential difference is applied to the plates the sphere is deflected through an angle θ as shown below. 10

11 (i) Calculate the electric field strength between the plates. 2 (ii) Calculate the electrostatic force acting on the sphere due to the electric field. 2 (iii) The mass of the sphere is kg. Calculate the magnitude and direction of the tension T in the supporting thread. 3 (c) The plates are now moved a short distance to the right without touching the sphere. The distance between the plates is unchanged. Does the angle θ increase, decrease or stay the same? Justify your answer. 2 (10) 2011 Q5 A helium-filled metal foil balloon with a radius of 0.35 m is charged by induction. The charge Q on the surface of the balloon is +120 μc. The balloon is considered to be perfectly spherical. (a) (i) Using diagrams, or otherwise, describe a procedure to charge the balloon by induction so that an evenly distributed positive charge is left on the balloon. 2 (ii) Calculate the electric field strength at the surface of the balloon. 2

12 (iii) Sketch a graph of the electric field strength against distance from the centre of the balloon to a point well beyond the balloon s surface. No numerical values are required. 1 (b) Two parallel charged plates are separated by a distance d. The potential difference between the plates is V. Lines representing the electric field between the plates are shown below. (i) By considering the work done in moving a point charge q between the plates, derive an expression for the electric field strength E between the plates in terms of V and d. 2 (ii) The base of a thundercloud is 489 m above an area of open flat ground as shown below. The uniform electric field strength between the cloud and the ground is 7.23 X 10 4 NC 1. Calculate the potential difference between the cloud and the ground. 1 (iii) During a lightning strike a charge of 5.0C passes between the cloud the potential of the cloud. Calculate the average power of the lightning strike. 2 12

13 (c) An uncharged metal foil balloon is released and floats between the thundercloud and ground, as shown below. Draw a diagram showing the charge distribution on the balloon and the resulting electric field around the balloon. 2 (12)

14 2010 Q6 A hollow metal sphere, radius 1.00 mm, carries a charge of C. (a) Calculate the electric field strength, E, at the surface of the sphere. 2 (b) Four students sketch graphs of the variation of electric field strength with distance from the centre of the sphere as shown below. (i) Which student has drawn the correct graph? 1 (ii) Give two reasons to support your choice. 2 (a) Four point charges, Q1, Q2, Q3 and Q4, each of value C, are held in a square array. The hollow sphere with charge C is placed 30.0 mm above the centre of the array where it is held stationary by an electrostatic force. 14

15 The hollow sphere is 41.2 mm from each of the four charges as shown below. (i) Calculate the magnitude of the force acting on the sphere due to charge Q1. 2 (ii) Calculate the vertical component of this force. 2 (iii) Calculate the resultant electrostatic force on the sphere due to the whole array. 1 (i) Calculate the mass of the sphere. 2 (12) 2008 Q5 (a) Two point charges Q1 and Q2 each has a charge of 4.0 μc. The charges are 0.60 m apart as shown below. (i) Draw a diagram to show the electric field lines between charges Q1 and Q2. 1

16 (ii) Calculate the electrostatic potential at point X, midway between the charges. 2 (b) A third point charge Q3 is placed near the two charges as shown below (i) Show that the force between charges Q1 and Q3 is 1.2N. 2 (ii) Calculate the magnitude and direction of the resultant force on charge Q3 due to charges Q1 and Q2. 2 (7) 2008 Q8 (a) Two protons are separated by a distance of 22 μm. (i) Show by calculation that the gravitational force between these protons is negligible compared to the electrostatic force. 4 (ii) Why is the strong force negligible between these protons? 1 (b) A particle of charge q travels directly towards a fixed stationary particle of charge Q. At a large distance from charge Q the moving particle has an initial velocity v. The moving particle momentarily comes to rest at a distance of closest approach rc as shown below. 16

17 Show that the initial velocity of the moving particle is given by where the symbols have their usual meaning. 2 (c) An alpha particle is fired towards a target nucleus which is fixed and stationary. The initial velocity of the alpha particle is ms 1 and the distance of closest approach is m. 3 (i) Calculate the charge on the target nucleus. 2 (ii) Calculate the number of protons in the target nucleus. 1 (iii) The target is the nucleus of an element. Identify this element. 1 (13) 2007 Q 5 (a) The figure below shows a point charge of +5.1nC. Point A is a distance of 200 mm from the point charge. Point B is a distance of 300 mm from point A as shown above. (i) Show that the potential at point A is 230V. 1 (ii) Calculate the potential difference between A and B. 2 (b) A conducting sphere on an insulating support is some distance away from a negatively charged rod as shown in Figure 6.

18 Using diagrams, or otherwise, describe a procedure to charge the sphere positively by induction. 2 (c) A charged oil drop of mass kg is stationary between two horizontal parallel plates. There is a potential difference of 4.9 kv between the parallel plates. The plates are 80 mm apart as shown below. (i) Draw a labelled diagram to show the forces acting on the oil drop. 1 (ii) Calculate the charge on the oil drop. 3 (iii) How many excess electrons are on the oil drop? 1 (d) The results of Millikan s oil drop experiment led to the idea of quantisation of charge. A down quark has a charge of C. Explain how this may conflict with Millikan s conclusion. 1 (11) 2006 Q5 (a) A charged metal sphere has a diameter of 0.36m. The electrostatic potential at the surface of the sphere is X 10 5 V. (i) Show that the charge on the sphere is +5.6 X 10 6 C. 2 (ii) State the electrostatic potential at a point 0.10m from the centre of the sphere. 1 (iii) i. Calculate the electric field strength at the surface of the sphere. 18

19 ii. Sketch a graph of the electric field strength against distance from the centre of the sphere to a point well beyond the sphere s surface. No numerical values are required. 3 (b) Two identical spheres, each carrying a charge of 5.6 X 10-6 C, are now placed as shown below. Point P is 0.60m vertically above the mid-point of the line joining the centres of the two spheres. Determine the magnitude and direction of the electric field strength at point P. 4 (10) TUTORIAL 4 Charges in Motion Q1 (a) Calculate the acceleration of an electron in a uniform electric field of strength 1.2 x 106 V m -1. (b) An electron is accelerated from rest in this electric field. (i) How long would it take for the electron to reach a speed of 3.0 x 10 7 m s -1? (ii) Calculate the displacement of the electron in this time Q2 In a Millikan type experiment a very small oil drop is held stationary between the two plates.

20 The mass of the oil drop is 4.9 x kg. (a) State the sign of the charge on the oil drop. (b) Calculate the size of the charge on the oil drop. Q3 An α-particle travels at a speed of 5.0 x 10 6 m s -1 in a vacuum. (a) Calculate the minimum size of electric field strength necessary to bring the α-particle to rest in a distance of 6.0 x 10-2 m. (The mass of an α-particle is 6.7 x kg). (b) Draw a sketch of the apparatus which could be used to stop an α- particle in the way described above. (c) Can a γ-ray be stopped by an electric field? Explain your answer. Q4 In an oscilloscope an electron enters the electric field between two horizontal metal plates. The electron enters the electric field at a point midway between the plates in a direction parallel to the plates. The speed of the electron as it enters the electric field is 6.0 x 10 6 m s -1. The electric field strength between the plates is 4.0 x 10 2 V m -1. The length of the plates is 5.0 x 10-2 m. The oscilloscope screen is a further 0.20 m beyond the plates. (a) Calculate the time the electron takes to pass between the plates. (b) Calculate the vertical displacement of the electron on leaving the plates. (c) Calculate the final direction of the electron on leaving the plates. (d) What is the total vertical displacement of the electron on hitting the oscilloscope screen. 20

21 Q5 Electrons are accelerated through a large potential difference of 7.5 x 10 5 V. The electrons are initially at rest. Calculate the speed reached by these electrons. Q6 In the Rutherford scattering experiment α-particles are fired at very thin gold foil in a vacuum. On very rare occasions an α-particle is observed to rebound back along its incident path. (a) Explain why this is not observed very often. (b) The α-particles have a typical speed of 2.0 x 10 7 m s -1. Calculate the closest distance of approach which an α-particle could make towards a gold nucleus in a head-on collision. The atomic number of gold is 79. The mass of the α-particle is 6.7 x kg. Q7 In Millikan's experiment, a negatively charged oil drop of radius 1.62 x 10-6 m is held stationary when placed in an electric field of strength 1.9 x 10 5 V m -1. (The density of the oil is 870 kg m -3, and the volume of a sphere is 4 /3 π r 3.) (a) Calculate the mass of the oil drop. (b) Calculate the charge on the oil drop. (c) How many electronic charges is your answer to (b) equivalent to? Q8 A charged particle has a charge-to-mass ratio of 1.8 x C kg -1. Calculate the speed of one such particle when it has been accelerated through a potential difference of 250 V.

22 Past paper question 2010 Q8 Identification of elements in a semiconductor sample can be carried out using an electron scanner to release atoms from the surface of the sample for analysis. Electrons are accelerated from rest between a cathode and anode by a potential difference of 2.40kV. A variable voltage supply connected to the deflection plates enables the beam to scan the sample between points A and B shown in Figure 8A. (a) Calculate the speed of the electrons as they pass through the anode. 2 (b) Explain why the electron beam follows (i) a curved path between the plates; 1 (ii) a straight path beyond the plates. 1 When the potential difference across the deflection plates is 100V, the electron beam strikes the sample at position A. (c) The deflection plates are 15.0 mm long and separated by 10.0mm. (i) Show that the vertical acceleration between the plates is ms 2. 2 (ii) Calculate the vertical velocity of an electron as it emerges from between the plates. 3 (c) The anode voltage is now increased. State what happens to the length of the sample scanned by the electron beam. 22

23 You must justify your answer. 2 (11) 2006 Q6 The print head of an ink jet printer fires a tiny drop of ink of mass 1.2 X kg as it scans across the paper. The drop carries a charge of -1.6 X C and enters the space between a pair of parallel plates at a speed of 20 ms -1 as shown below. The length of the plates is 7.5 X 10-3 m and the electric field strength between them is 2.5 X 10 4 N C -1. (a) Calculate the magnitude of the electrostatic force acting on the ink drop as it passes between the plates. 2 (b) Show by calculation that the gravitational force acting on the drop is negligible compared to the electrostatic force. 2 (c) Calculate the deflection s of the drop as it leaves the region between the plates. 4 (d) Calculate the number of excess electrons on the ink drop. 2 (10)

24 TUTORIAL 5 Force on a Conductor Q1 A straight wire, 0.05 m long, is placed in a uniform magnetic field of magnetic induction 0.04 T. The wire carries a current of 7.5 A, and makes an angle of 60 with the direction of the magnetic field. (a) Calculate the magnitude of the force exerted on the wire. (b) Draw a sketch of the wire in the magnetic field and show the direction of the force, (c) Describe the conditions for this force to be a maximum. Q2 A straight conductor of length 50 mm carries a current of 1.4 A. The conductor experiences a force of 4.5 x 10-3 N when placed in a uniform magnetic field of magnetic induction 90 mt. Calculate the angle between the conductor and the direction of the magnetic field. Q3 A wire of length 0.75 m and mass kg is suspended from two very flexible leads as shown below. The wire is in a magnetic field of magnetic induction 0.50 T. As the sketch shows, the magnetic field direction is into the page. (a) Calculate the size of the current in the wire necessary to remove the tension in the supporting leads. (b) Copy the sketch and show the direction of the electron current which produced this result. 24

25 Q4 The sketch below shows the rectangular coil of an electric motor. The coil has 120 turns and is 0.25 m long and 0.15 m wide and carries a current of 0.25 A. It lies parallel to a magnetic field of magnetic induction 0.40 T. The sketch shows the directions of the forces acting on the coil. (a) Calculate the magnitude of the force, F, on each of the wires shown. (b) Calculate the torque which acts on the coil when in this position. (c) State and explain what will happen to this torque as the coil starts to rotate in the magnetic field. Q5 The diagram below shows a force-on-a-conductor balance set up to measure the magnetic induction between two flat magnets in which a north pole is facing a south pole. The length of the wire in the magnetic field is 0.06 m. When the current in the wire is zero, the reading on the balance is 95.6g. When the current is 4.0 A the reading on the balance is 93.2 g.

26 (a) Calculate the magnitude and direction of the force on the wire from these balance readings. (b) Calculate the size of the magnetic induction between the poles of the magnets. (c) Suggest what the reading on the balance would be if the connections to the wire from the supply were reversed. Explain your answer. (d) Suggest what the reading on the balance would be if one of the magnets is turned over so that the north face on one magnet is directly opposite the north face of the other magnet. Explain your reasoning. Q6 Two parallel wires 0.20 m apart carry large direct currents to an iron recycling plant. The large currents passing into the metal generate enough heat to make the iron melt. It can then be made into new shapes. (a) Calculate the force between two such wires 16 m long if they each carry a current of 2500 A. (b) Hence explain why these wires are not suspended freely on their route to the iron smelter. TUTORIAL 6 Charged Particles in Magnetic Fields Q1 A particle carrying a positive charge of 1.6 x C travels at 1.0 x 10 7 m s -1 and enters a magnetic field at an angle of 45. The force experienced by the particle is 3.0 x N. Calculate the size of the magnetic induction required to produce this result. 26

27 Q2 Close to the equator the horizontal component of the Earth's magnetic field has a magnetic induction of 3.3 x 10-5 T. A high energy proton arrives from outer space with a vertical velocity of 2.8 x 10 8 m s -1. Show that the ratio of the magnetic force, Fm, to gravitational force, Fg, experienced by the proton is given by Q3 Inside a bubble chamber, a proton is injected at right angles to the direction of the magnetic field of magnetic induction 0.28 T. The kinetic energy of the proton is 4.2 x J. Calculate the radius of the circle described by the track of the proton. Q4 An electron and an alpha particle both make circular orbits in the same magnetic field. Both particles have the same orbital speed. The mass of an alpha particle is 6.68 x kg. Calculate the ratio Q5 A cyclotron has an oscillator frequency of 1.2 x 10 7 Hz and a maximum effective dee radius of 0.50 m. The sketch below shows the geometry of the cyclotron. The deflector plate is mounted at the maximum radius of 0.50 m and its purpose is to ensure that the charged particles exit successfully. (a) Show that the frequency of rotation is given by (b) The cyclotron is used to accelerate deuterons from rest. Calculate the magnetic induction, of the magnetic field of the cyclotron, needed to

28 accelerate the deuterons. (A deuteron is an isotope of hydrogen, containing a proton and a neutron, with a mass of 3.34 x kg.) (c) Calculate the kinetic energy of the emerging deuterons. Q6 (a) Certain charged particles can be 'selected' from a beam of charged particles if they are made to enter crossed electric and magnetic fields. The directions of the fields are mutually perpendicular. Show that those particles with a velocity equal to the ratio will be undeflected. (b) A velocity selector such as that in (a) above has a magnetic induction of 0.70 T and an electric field strength of 1.4 x 10 5 V m -1. Calculate the velocity of the undeflected charged particles which pass through the crossed fields. (c) The sketch below shows a mass spectrometer arrangement used to deflect ions. After the exit slit from the velocity selector there is only a magnetic field present. (The final position of the ions is detected by a photographic plate). (i) Negatively charged neon ions, which carry one extra electron, emerge from the velocity selector into a uniform magnetic field of magnetic induction 0.70 T. The ions follow the semicircular path shown above. The radius of the circle is 70 mm. Calculate the mass of the neon ions. 28

29 (ii) Explain how the mass spectrometer can show the presence of different isotopes of neon. (Isotopes are nuclei having the same atomic number but different mass numbers). Q7 An alpha particle travels in a circular orbit of radius 0.45 m while moving through a magnetic field of magnetic induction 1.2 T. Calculate: (a) (b) (c) the speed of the alpha particle in its orbit the orbital period of the alpha particle the kinetic energy of the alpha particle in its orbit. Q8 The diagram below shows the Earth's magnetic field. Three positively charged particles, X, Y and Z approach the Earth along the directions shown. Path Y is perpendicular to the direction of the Earth s magnetic field lines. (a) For each of the particles, describe the path followed in the Earth's magnetic field. (b) A proton approaches the earth along path Y with a speed of 2.0 x 10 6 m s -1. Calculate the radius of the path of the proton at a point where the magnetic induction of the Earth is 1.3 x 10-5 T.

30 Q9. In an experiment to measure the charge to mass ratio for an electron, apparatus similar to that used below (a) Crossed electric and magnetic fields are applied to produce an undeflected beam. The current, I, in the Helmholtz coils is measured to be 0.31 A. The p.d., V, across the plates is 1200 V. (i) Show that the velocity, v, of the electrons between the plates is given by where d is the plate separation and B the magnetic induction. (ii) The magnetic induction, B, is given by where N, the number of turns, is 320 and a, the effective radius of the coils, is m. Calculate the magnetic induction B. (iii) The plate separation, d, is m. Calculate the magnitude of the velocity of the electrons. (b) The electric field is switched off and the above magnetic field only is applied. A deflection, y, of m is measured. (i) Show that the charge to mass ratio where r is the radius of the curved path of the electrons when only the magnetic field is applied. 30

31 (ii) The radius, r, is given by r = (L2 + y2)/2y where L, the length of the plates, is m. Calculate the charge to mass ratio for the electrons from this data. Q10 The sketch below shows the layout of the apparatus which allows crossed electric and magnetic fields to be applied to an electric beam. (The Helmholtz coils which produce the magnetic field 'into the paper' have been omitted for clarity). The screen is 0.05 m square. The length, L, and separation, d, are both 0.05 m. (a) With only the electric field switched on the p.d. between the plates is set at 1200 V. The vertical deflection, y, of the electron beam at the end of the plates is 1.0 cm. Calculate the electric field strength between the plates which provides this deflection. (b) (i) Both the electric and magnetic fields are now applied. The electron beam is undeflected when the current to the Helmholtz coils is 0.25 A. The coils have 320 turns and an effective radius of m. Using the expression calculate the value this gives for the magnetic induction between the plates.

32 (iii) Calculate the speed of the electrons as they enter the plates. (c) With the electric field only applied, the electron beam has a vertical deflection, y of 1.0 cm at the end of the plates. (i) Show that the deflection where a is the acceleration produced by the electric field and v is the speed of the electrons entering the plates as shown in the diagram. (ii) Using the data in the question, calculate a value for the charge to mass ratio, e/m, for the electron. Q11. Apparatus similar to that shown in question 10 is used in another experiment to determine the charge to mass ratio for the electron. The length of the plates L and their separation d are 0.05 m. In this experiment the p.d. across the electron gun is set at 1000 V. Assuming the electrons leave the cathode with zero speed, the speed of the electrons entering the plates can be determined using this electron gun potential difference. (a) Show that where v is the speed of the electrons as they leave the electron gun. (b) Both the electric and magnetic fields are applied to give an undeflected beam. The p.d. across the plates is 1000 V. The current in the Helmholtz coils to give an undeflected beam is measured to be 0.26 A. (i) Use the expression where the number of turns, N, is 320 and the effective radius r of the coils is m, to calculate the size of the magnetic induction between the plates. 32

33 (ii) Calculate the magnitude of the speed v of the undeflected electrons when they are between the plates. (c) Calculate the charge to mass ratio for the electrons from this data. (d) The overall uncertainty in this experiment was estimated to be 5 %. (i) Express the measured value of the charge to mass ratio as (value ± absolute uncertainty). (ii) Consider the accepted value and comment on the accuracy of this experiment. Past papers 2006 Q7 (a) (i) A Cyclotron is a particle accelerator which consists of two D-shaped hollow structures called dees placed in a vacuum. The figure below shows an arrangement for a cyclotron. The figure below shows a view of the cyclotron from above

34 Protons are released from rest point A and accelerated across the gap between the dees by a voltage of 2.00kV. Show that the speed of the protons as they first reach the rights hand dee is 6.19 X 10 5 ms -1. 2? (ii) Inside the dees the electricfield strength is zero but a uniform magnetic field of 1.30 T acts perpendicularly to the dees. This forces the protons to move in semi-circular paths when inside the dees. Calculate the radius of the first such path in the right hand dee. 3? (iii) (b) (c) While the protons are inside the dee the polarity of the applied voltage is reversed so that the protons are again accelerated when they cross to the left hand dee. Calculate the speed of the protons as they first enter the left hand dee 2 The protons exit the cyclotron with a kinetic energy of 1.57 X J and are aimed a at gold target. The charge on a gold nucleus is +79e. Find the distance of closest approach to a gold nucleus for a proton from this cyclotron. 3 A larger accelerator produces protons with a relativistic mass of 4.66 X kg. Calculate the speed of these protons. 2 (12) 34

35 2007 Q6 The shape of the Earth s magnetic field is shown below. At a particular location in Scotland the field has a magnitude of T directed into the Earth s surface at an angle of 69 as shown below. (a) Show that the component of the field perpendicular to the Earth s surface is T. 1

36 (b) At this location a student sets up a circuit containing a straight length of copper wire lying horizontally in the North South direction as shown below. The length of the wire is 1.5m and the current in the circuit is 3.0A. (i) Calculate the magnitude of the force acting on the wire due to the Earth s magnetic field. 2 (ii) State the direction of this force. 1 (c) The wire is now tilted through an angle of 69 so that it is parallel to the direction of the Earth s magnetic field. Determine the force on the wire due to the Earth s magnetic field. 1 (d) A long straight current carrying wire produces a magnetic field. The current in this wire is 3.0A. (i) Calculate the distance from the wire at which the magnitude of the magnetic field is T. 2 (ii) Describe the shape of this magnetic field. 1 (8) 36

37 2007 Q8 An electron travelling at ms 1 enters a uniform magnetic field B at an angle of 60 as shown below. (a) The electron moves in a helical path in the magnetic field. (i) Calculate the component of the electron s initial velocity: (A) parallel to the magnetic field; 1 (B) perpendicular to the magnetic field. 1 (ii) By making reference to both components, explain why the electron moves in a helical path. 2 (b) (i) The magnetic field has a magnetic induction of 0.22T. Show that the radius of the helix is m. 2 (ii) Calculate the time taken for the electron to make one complete revolution. 2 (iii) The distance between adjacent loops in the helix is called the pitch as shown in the figure above. Calculate the pitch of the helix. 2 (d) A proton enters the magnetic field with the same initial speed and direction as the electron shown in the figure above. The magnetic field remains unchanged. State two ways that the path of the proton in the magnetic field is different from the path of the electron. 2 (12)

38 2009 Q5 An alpha particle passes through a region that has perpendicular electric and magnetic fields, as shown below. The magnetic induction is 6.8T and is directed out of the page. The force on the alpha particle due to the magnetic field is N. (a) Show that the velocity of the alpha particle is ms 1. 2 (b) In order that the alpha particle exits through slit S, it must pass through the region undeflected. Calculate the strength of the electric field that ensures the alpha particle exits through slit S. 2 (c) After passing through slit S, the alpha particle enters a region where there is the same uniform perpendicular magnetic field but no electric field as shown below. This magnetic field causes the alpha particle to travel in a semi-circular 38

39 path and hit the detector surface. Points A, B and C are at distances of m, 0.14 m and 0.28m respectively from slit S. Show, by calculation, which point on the detector surface is hit by the alpha particle. 3 (d) An electron travelling at the same speed as the alpha particle passes through slit S into the region of uniform magnetic field. State two differences in the semi-circular path of the electron compared to the path of the alpha particle. Justify your answer. 3 (10) 2010 Q7 A beam of protons enters a region of uniform magnetic field, at right angles to the field. The protons follow a circular path in the magnetic field until a potential difference is applied across the deflecting plates. The deflected protons hit a copper target. The protons travel through a vacuum. A simplified diagram is shown below. (a) State the direction of the magnetic field, B. 1

40 (b) The speed of the protons is ms 1 and the magnetic induction is 0.75T. Calculate the radius of the circular path followed by the protons. 3 (c) Calculate the electric field strength required to make the protons move off at a tangent to the circle. 2 (d) A proton of charge q initially travels at speed v directly towards a copper nucleus as shown below. The copper nucleus has charge Q. (i) Show that the distance of closest approach, r, to the copper nucleus is given by 1 (ii) Calculate the distance of closest approach for a proton initially travelling at ms 1. 3 (iii) Name the force that holds the protons together in the copper nucleus. 1 (e) The beam of protons is replaced by a beam of electrons. The speed of the electrons is the same as the speed of the protons. State two changes that must be made to the magnetic field to allow the electrons to follow the same circular path as the protons. 2 (13) 40

41 2011Q7 (a) Two very long straight wires X and Y are suspended parallel to each other at a distance r apart. The current in X is I1 and the current in Y is I2 as shown below. (i) State the direction of the magnetic force acting on wire X. Justify your answer. 2 (ii) The wires are separated by a distance of 360 mm and each wire carries a current of 4.7A. Calculate the force per unit length which acts on each wire. 2 (b) A student investigating the force on a current carrying wire placed perpendicular to a uniform magnetic field obtains the following measurements and uncertainties. (i) From this data, calculate the magnetic induction, B. 3 (ii) Calculate the absolute uncertainty in the value of the force. 3 (iii) Calculate the overall absolute uncertainty in the value of the magnetic induction. 3 (13)

42 2011Q8 (a) The figure below shows a current carrying wire of length l, perpendicular to a magnetic field B. A single charge q moves with constant velocity v in the wire. Using the relationship for the force on a current carrying conductor placed in a magnetic field, derive the relationship F = qvb for the magnitude of the force acting on charge q. 2 (b) An electron with a speed of ms 1 enters a uniform magnetic field at an angle θ. The electron follows a helical path as shown below. The uniform magnetic induction is 3.6 mt and the radius of the helical path is 2.8 mm. Calculate the value of angle θ. 3 (c) A second electron travelling at the same speed enters the field at a smaller angle θ. Describe how the path of the second electron differs from the first. 2 (7) 42

43 2012 Q6 A positively charged particle travelling at m s 1 enters a magnetic field of uniform magnetic induction 2 50 T as shown below The direction of the magnetic field is out of the page. The particle follows a semicircular path before exiting the field. (a) (i) State whether the particle will exit the field at point P or point Q. 1 (ii) Show that the charge to mass ratio of the particle is given by where the symbols have their usual meaning. 1 (iii) The radius of the path taken by the particle is 19 0 mm. Use information from the data sheet to identify the charged particle. You must justify your answer by calculation. 3 (iv) Calculate the time between the particle entering and leaving the magnetic field. 2 (v) An identical particle travelling at twice the speed of the original particle enters the field at the same point. How does the time spent in the magnetic field by this particle compare with the original? Justify your answer. 2

44 (b) An unknown particle also travelling at m s 1 enters the field as shown below. The path taken by this particle is shown. What can you conclude about: (i) the charge of the unknown particle; 1 (ii) the charge to mass ratio of the unknown particle? 1 (11) 2012 Q8 A long thin horizontal conductor AB carrying a current of 25 A is supported by two fine threads of negligible mass. The tension in each supporting thread is T as shown below. (a) Calculate the magnetic induction at a point P, 6 0 mm directly below conductor AB. 2 44

45 (b) A second conductor CD carrying current I is now fixed in a position a distance r directly below AB as shown below. CD is unable to move. (i) Explain why there is a force of repulsion between conductors AB and CD. 2 (ii) Show that the force per unit length acting on each conductor can be written as 1 (iii) The mass per unit length of the conductor AB is kg m 1. When the conductors are separated by 6 0 mm, the current I in conductor CD is gradually increased. Calculate the value of I which reduces the tension in the supporting threads to zero. 3 (8) TUTORIAL 7 Self Inductance Q1 The sketch below shows an inductor connected to a 12 V direct supply of negligible internal resistance. The resistance of the coil is 1 Ω (as shown). When switched on the current grows from zero. The rate of growth is 400 A s -1 when the current is 8.0 A. (a) Calculate the induced e.m.f. across the coil when the current is 8 A.

46 (b) Calculate the inductance of the coil. (c) Calculate the rate of increase of current when the switch is closed. (d) A final steady value of current is produced in the coil. Find the value of this current. (e) Calculate the final energy stored in the inductor. Q2 An inductor with a removable soft iron core is connected in series with a 3.0 V direct supply of negligible internal resistance as shown below. A milliammeter is used to monitor the current in the circuit. The switch is closed. The graph above shows the variation of current with time. (a) (i) Explain why it takes some time for the current to reach its maximum value. (ii) Why does the current remain constant after it reaches its maximum value. (b) The soft iron core is then partly removed from the coil and the experiment repeated. Draw a sketch graph showing how the current varies against time for this second experiment. Use the same numerical values on the axes as those in the graph above. (c) Calculate the resistance of the coil. 46

47 Q3 In the circuit shown below, the resistance of resistor R is 40 Ω and the inductance of inductor L is 2.0 H. The resistance of the inductor may be neglected. The supply has an e.m.f. of 10 V and a negligible internal resistance. (a) Immediately after the switch is closed: (i) state the p.d. across the 40 Ω resistor (ii) calculate the size of the current (iii) state the induced e.m.f. across the 2.0 H inductor (iv) calculate the energy stored in the inductor. (b) Some time later the current reaches a value of A. (i) At this time, calculate the p.d. across R. (ii) Calculate the p.d. across the inductor at this time. (iii) Hence calculate the rate of growth of current when the current in the circuit is A. (iv) Calculate the energy stored in the inductor. Q4 (a) Describe what is meant by the self-inductance of a coil. (b) The circuit diagram below shows a resistor, inductor and two lamps connected to a direct supply of 10 V. The supply has negligible internal resistance. The rating of each lamp is 6 V, 3 W.

48 After the switch is closed each lamp operates at its rated power. However lamp Y lights up before lamp X. (i) Explain why lamp Y lights before lamp X. (ii) (iii) The current in lamp X grows at a rate of 0.50 A s -1 just as the switch is closed. Calculate the inductance of the coil. Calculate the resistance of the coil. Q5. The diagram below shows the principle of the spark plug for a car engine. The cam, which is rotated by the engine, makes and breaks contact at S. This switches on and off the current to the primary of a transformer. When the contact at S is opened a high voltage spark of around 20 kv is induced across the spark plug. (a) Explain why a voltage is induced across the spark plug particularly when S is opened. (b) Explain whether a step-up or step-down transformer would be more useful in this case. (c) Where does the energy for the spark come from? Q6 The magnet in the sketch below is mounted like a pendulum. It is allowed to swing to and fro into and out of a coil which has N turns. 48

49 (a) Sketch a graph to show the variation of induced e.m.f. with time as the pendulum magnet swings to and fro. (b) What is the induced e.m.f. when the magnet momentarily stops? (c) State what happens to the induced e.m.f. as the magnet reverses its direction of movement. (d) What happens to the induced e.m.f. at the positions where the magnet moves fastest? Q7 A circuit is set up as shown below. The a.c. supply is of constant amplitude but variable frequency. The frequency of the supply is varied from a very low frequency to a very high frequency. Explain what you would expect to happen to the average brightness of each of the lamps X, Y and Z as the frequency is increased. Q8 The output from an amplifier is connected across XY in the circuit shown below. This is designed to direct low frequency signals to one loudspeaker and high frequency signals to the other loudspeaker. (a) Suggest which of the loudspeakers A or B is intended to reproduce high frequency signals. (c) Explain how the high and low frequency signals are separated by this circuit.

50 Past papers 2006 Q8 A datalogger is used to investigate the rate of change of current in the circuit shown (a) The datalogger measures the potential V A and the potential V B. What other piece of information is required to allow the computer software to determine the current in the circuit? 1 (b) The switch S is closed and datalogger software produces the graph shown below. Assuming that the resistance is negligible, calculate its inductance. 2 (c) The current in the circuit eventually reaches a steady value of 100 ma. Calculate the energy stored in the magnetic field of the inductor. 2 (d) The diode in the circuit is necessary to protect the datalogger against the higher voltage which can arise when the switch S is opened. Explain why this high voltage is produced. 1 (6) 50

51 2007 Q7 (a) The figure below shows a d.c. power supply in series with a switch, lamp and inductor. The inductor consists of a coil of wire with a resistance of 12 Ω. The lamp is rated at 6.0 V 1.5 W. The 9.0 V power supply has a negligible internal resistance. (c) (d) (e) (f) Explain why the lamp does not reach its maximum brightness immediately after the switch is closed. 2 When the lamp reaches its maximum brightness it is operating at its stated power rating. Calculate the current in the circuit. 1 The maximum energy stored in the inductor is 75 mj. Calculate the inductance of the inductor. 2 The inductor is replaced with another inductor which has the same type of core and wire, but twice as many turns. State the effect this has on: (a) the maximum current (b) the time to reach maximum current 2

52 (b) The figure below shows a neon lamp connected to an inductor, switch and a 1.5 V cell. A neon lamp needs a potential difference of at least 80 V across it before it lights. The switch is closed for 5 seconds. The switch is then opened and the neon lamp flashes briefly. Explain this observation. 2 (9) 52

53 2008 Q7 An inductor of negligible resistance is connected in the circuit shown below (a) The inductor has an inductance of 0.80 H. Switch S is closed. (i) Explain why there is a time delay before the current reaches its maximum value. 1 (ii) Calculate the maximum current in the circuit. 2 (iii) Calculate the maximum energy stored in the inductor. 2 (iv) Calculate the rate of change of current when the current in the circuit is 0.12 A. 3 (b) Switch S is opened and the iron core is removed from the inductor. Switch S is now closed. (i) Will the maximum current be bigger, smaller or the same as the maximum current calculated in (a)(ii)? 1 (ii) Explain any change in the time delay to reach the maximum current. 2 (iii) Explain why the maximum energy stored in the inductor is less than in (a)(iii). 1

54 (c) The iron core is replaced in the inductor. The d.c. supply is replaced with a variable frequency supply as shown below. Sketch a graph to show how the current in the circuit varies with the frequency of the supply. Numerical values are not required. 1 (13) 54

55 2009 Q6 (a) A 3.0V battery is connected in series with a switch, a resistor and an inductor of negligible resistance. A neon lamp is connected across the inductor as shown in below. (ii) (iii) (iii) (iv) Sketch a graph to show how the current in the inductor varies With time from the instant the switch is closed. 2 Appropriate numerical values are required on the current axis. The neon lamp requires a potential difference of at least 110V across it before it lights. 1 Explain why the lamp does not light when the switch is closed. After a few seconds the switch is opened and the lamp flashes. Explain, in terms of the magnetic field, why the lamp flashes as the switch is opened. 2 The neon lamp has an average power of 1.2 mw and a flash that lasts 0.25 s. Assuming all the energy stored by the inductor is transferred to the lamp, calculate the inductance of the inductor. 3

56 (b) Figure 6B shows a circuit used to investigate the relationship between the current in an inductive circuit and the supply frequency. The reading on the ammeter is noted for different values of supply frequency. (i) State the purpose of the voltmeter. 1 (ii) Describe how the data obtained should be analysed to determine the relationship between the current in the inductive circuit and the supply frequency. 1 (iv) State the expected relationship. 1 (b) A loudspeaker system is connected to a music amplifier. The system contains a capacitor, inductor and two loudspeakers, LS1 and LS2, as shown below. The circuit is designed so that one loudspeaker emits low frequency sounds while the other emits high frequency sounds. By comparing the capacitive and inductive reactances, describe the operation of this system. 2 (13) 56

57 2011 Q6 Modern trains have safety systems to ensure that they stop before the end of the line. One system being tested uses a relay operated by a reed switch. The reed switch closes momentarily as it passes over a permanent magnet laid on the track. An inductor in the relay activates the safety system as shown below. (a) (i) Explain why there is a short time delay between the reed switch closing and the relay activating. 2 (ii) The inductor is connected to a 12.0V d.c. supply. The inductor has an inductance of 0.6H and the total resistance of the circuit is 28Ω. Calculate the initial rate of change of current as the reed switch is closed. 2 (iii) The inductance of the inductor on the train is 0.6 H. Define one henry. 1 (v) The reed switch opens as it moves away from the permanent magnet. Explain why a spark occurs across the contacts of the reed switch. 2 (v) A diode is placed across the inductor to prevent sparks across the reed switch as it opens as shown in Figure 6B. The diode must be chosen to carry the same current as the maximum current which occurs in the circuit when the reed switch closes. Calculate this current. 1

58 (b) Another safety system prevents trains approaching a stop signal at excessive speed. When a train is travelling too fast the brakes are applied automatically and the train is brought uniformly to rest. An inductor at the front of the train is used to determine the average speed as it travels between the electromagnets 1 and 2 as shown below. The train travels between the electromagnets at a constant speed of 99kmh 1. The brakes are applied automatically as the train passes the second electromagnet. The train is accelerated at 1.0ms 2. Show by calculation whether the train stops before the signal. 2 (c) The train is stopped and a passenger hears a siren on another train approaching along a parallel track. The approaching train is travelling at a constant speed of 28.0ms 1 and the siren produces a sound of frequency 294 Hz. (i) Show that the frequency f of the sound heard by the passenger is given by where symbols have their usual meaning. 2 (ii) Calculate the frequency of the sound heard by the passenger: (A) as the train approaches; 1 (B) once the train has passed the passenger. 2 (15) 58

59 2012 Q7 Precision inductors can be produced using laser technology. A thin film of copper is deposited on a ceramic core. A carbon dioxide laser is then used to cut the copper to form a coil as shown in below. (a) Each photon from the laser has a momentum of kg m s 1. (i) Calculate the wavelength of each photon. 2 (ii) The inductor has an inductance of 0 1 H. Explain what is meant by an inductance of 0 1 H. 1 (b) The rate of change of current for a different inductor is investigated using a datalogger as shown in below. This inductor has inductance L and a resistance of 2Ω.

60 The graph shown in Figure 7C shows how the rate of change of current di/dt in the circuit varies with time from the instant switch S is closed. (i) Describe what happens to the magnetic field strength associated with the inductor between 0 and 1 6 s. 1 (ii) Use information from the graph to determine the inductance L. 2 (iii) (iv) Sketch a graph to show how the voltage across the 8 Ω resistor varies during this time. Numerical values are required on both axes. 2 Calculate the maximum energy stored by the inductor in this circuit. 2 (c) A student sets up the circuit shown below to investigate the relationship between current and frequency for a capacitor and for an inductor. At frequency of 75 Hz the readings on A1 and A2 are the same. Explain what happens to the readings on each ammeter as the frequency is increased from 75 Hz to 150 Hz. Assume that the supply voltage remains constant. 2 (12) 60

61 Tutorial 8 Forces of Nature Q1 (a) (i) Calculate the electrostatic force between two protons in the nucleus of iron. Assume a separation of 4.0 X m between the protons. (b) (ii) (i) (ii) (iii) (iv) Is this force attractive or repulsive? Calculate the gravitational attraction between two protons separated by 4.0 X m. Is this force attractive or repulsive? Is this force large enough to balance the electrostatic force between the protons? Hence explain why the iron nucleus does not fly apart. Q2 (a) Briefly state the difference between the strong and weak nuclear forces. (b) Give an example of a particle decay associated with the weak nuclear force. (c) Comment on the range of the strong and weak nuclear forces. Q3 Neutron and protons are considered to be composed of quarks. (a) How many quarks are in each particle? (b) Briefly comment on the different composition of the neutron and proton.

62 Q Q9 (a) According to modern particle theory, protons and neutrons are composed of combinations of up and down quarks. Up qualrks have a charge of + 2/3 e while down quarks have a charge of 1/3 e. i. Name the force which holds the quarks together in protons and neutrons. 1 ii. State the combination of up and down quarks which make up: (a) a proton (b) a neutron 2 (b) A neutron can decay into a proton, electron and antineutrino. Name the force associated with this decay. 1 (c) A thermal neutron has a velocity of 3.5 X 10 3 ms -1. Calculate the de Broglie wavelength of this neutron. 2 (6) 62

63 2009 Q4. (a) A point charge of +4.0 μc is shown in below. (i) Copy the above figure and draw the electric field lines around this point charge. 1 (ii) A point charge of 2.0 μc is now placed at a distance of 0.10 m from the first charge as shown in below. Explain why the electric field strength is not zero at any point between these two charges. 2 (iii) Point P is 0.24 m to the right of the second charge as shown below. Calculate the electric field strength at point P. 3 (b) Two like charges experience a repulsive electrostatic force. Explain why two protons in a nucleus do not fly apart. 2 (c) Information on the properties of three elementary particles together

64 with two types of quarks and their corresponding antiquarks is shown in the tables below. (i) Using information from the tables, show that a proton consists of two up quarks and one down quark. 1 (ii) State the combination of quarks that forms a pi-meson. 1 (10) 64

65 CSYS 1994 Q 6 The figure below shows an ideal inductor in series with a resistor. a) Calculate the self-inductance L given that the initial rate of change when the switch is closed is 2.0 A s b) (i) What is the maximum current in the circuit? 2 (ii) Sketch a graph showing how the current varies with time for this circuit. 2 c) The experiment is repeated with the iron core removed. Describe how the graph or current against time would differ from your answer in b) (ii). 2 (8)

66 CSYS 1995 Q12 d The relationship induction occurs in electromagnetic (a) Comment on the significance of the minus sign in the relationship. 1 (b) Define the henry, the unit of inductance of an inductor 1 (c) Sketch a graph showing how current varies with time after the switch is closed in a d.c. circuit containing an inductor. 1 (d) A coil of self inductance L and negligible resistance is connected in series with a resistor or resistance R = 25 Ω as shown in the figure below. The battery has an e.m.f. of 12.0 V and a negligible internal resistance. A short time after closing the witch, the current is 0.22 A and the rate of change of current in the circuit is 0.90 A s -1. Calculate the inductance of the coil. 1 (5) 66

67 CSYS 1998 Q6 An inductor is connected in series with a resistor and a 3.0 V battery. (a) (i) (ii) State the initial voltage across the inductor after the switch S is closed. Calculate the maximum current in the circuit. (b) Sketch a graph showing how the current varies with time from the moment when the switch is closed. (4)

68 Inductive reactance CSYS 1995 Q15 Analogue electronics (a) (i) A capacitor of capacitance C is connected to an a.c. supply whose e.m.f. is represented by V = V m sin ωt, where V and V m are the instantaneous and peak e.m.f.s respectively. Derive an expression for the reactance X c of the capacitor. (ii) A coupling capacitor allows an a.c. signal to pass to the second stage of an amplifier but prevents any d.c. component from affecting it. Callulate the reactance of a coupling capacitor of 10 µf capacitance for a signal frequency of 200Hz. (iii) A capacitor is connected in series with a resistor of resistance R to an a.c. supply e.m.f. V = V m sin ωt as shown below (b) Using a phasor diagram or otherwise, derive the impedance of this circuit in terms of R and X c. 6 (i) Draw two RC circuits, one showing a low pass filter and the other a high pass filter. Your circuit diagrams should show clearly between which points in the circuit the input voltage V in is applied and the output voltage V out appears. (ii) Explain clearly how the RC network acts as a low pass filter. (iii) For a low pass filter, the output and input voltages are linked by the expression A low pass filter is made up of a capacitor of 15nF capacitance and a resistor of 1.0 kω resistance. Calculate the voltage gain in decibels when the frequency of the input voltage is 10 khz. 7 68

69 (c) (i) (ii) Draw a circuit showing an op-amp used as an intergrator. For this circuit, show that the output and input voltages are related by the expression 5 (d) Maximum power is transferred from an audio amplifier to a loudspeaker when the output impedance of the amplifier and the loudspeaker impedance are matched. An audio amplifier has an output impedance of 2.0 kω and is to be matched to a loudspeaker of impedance 4.0 Ω using a transformer. Calculate the turns ratio of the transformer. 2 (20) CSYS 1999 Q (a) A capacitor, inductor and resistor are connected in series to a signal generator as shown below The reactance of the capacitor and inductor are given by (i) Draw a diagram to show the phase relationship for the voltages V L, V C, V R and the current I in the circuit. (ii) Hence or otherwise show that the resonant frequency f o is given by 4 (b) As part of an LCR circuit investigation, a student uses the circuit shown above in part (a). He uses a 10 µf capacitor, an inductor and a 20 Ω

70 resistor. He varies the frequency of the supply and by measuring appropriate values of frequency and current he is able to plot the current frequency graph shown below. For this investigation determine (i) (ii) (iii) (iv) the resonant frequency the bandwidth the Q factor the inductance of the inductor. 7 70

71 (c) The student now changes the values of the capacitor and resistor in the circuit as shown in part (a) and repeats the experiment to obtain the graph shown below. What change in the value of the capacitor alters the graph shown in part (b) to that shown in part (c)? Give a reason for you answer. 2 (d) A medium wave radio transmitter uses a carrier wave of frequency 648 khz. Audio frequencies in the range 50Hz to 12kHz are transmitted using this carrier wave. Calculate (i) The minimum bandwidth of the a.m. signal (ii) The frequency range of the upper sideband. 4 (e) Draw a block diagram of the systems contained within a simple a.m. radio transmitter to include the following: Aerial; a.f. amplifier; master r.f. oscillator; microphone; modulator / mixer; r.f. amplifier; r.f. power amplifier. 3 (20)

72 CSYS 2000 Q14 (e) The circuit below shows a high pass filter. (a) Explain why this circuit passes high frequencies better than low frequencies. (b) The gain for this filter is given by Calculate the gain in decibels if C = 1.0 µf, R = 1.0 kω and the frequency of the input voltage is 50Hz. (c) What change could be made to this circuit to make it a low pass filter? (4) CSYS 1997 Q15 (a) (a) The figure below shows a diagram of a parallel LC circuit which is used to investigate electrical oscillations. Switch S is opened after being closed for a short time. (i) On square ruled paper, draw the trace which would be obtained on the cathode ray oscilloscope screen. (ii) A resistor is added to the LC circuit. 72

73 (iii) On new axes, using the same scale, draw the trace which would be obtained on repeating the experiment. (iv) The number of turns of wire on the inductor L is increased. On new axis using the same scale, draw the trace which would be obtained on repeating the experiment. Describe how the oscillations in the LC circuit could be maintained. (4) Electron Volt 1 What is meant by the term one electron volt? 2 The energy to accelerate a proton in the Large Hadron Collider is 7.2 TeV (7.2 X ev). What is this in joules? Ferromagnetism 1 Draw the magnetic filed lines around this magnet. N S 2 Draw the magnetic field lines around the earth.