MAGNETIC EFFECT OF CURRENT

MAGNETIC EFFECT OF CURRENT VERY SHORT ANSWER QUESTIONS Q.1 Who designed cyclotron? Q.2 What is the magnetic field at a point on the axis of the current element? Q.3 Can the path of integration around which we apply Ampere s law pass through a conductor? Q.4 Give the dimensional formula of μ0. Q.5 What is the value of 4? 0 Q.6 Which of the three has lowest resistance ammeter, voltmeter, galvanometer? Q.7 An electron is moving through a field but is not experiencing any force. Are you sure that the field that we are talking about is not an electric field? Q.8 Does the equation B=μ0nI hold for a solenoid of square cross-section? Q.9 Name the type of galvanometers commonly used in experiments. Q.10 What is the direction of the force between two parallel wires carrying current Q.11 A negative charge is moving vertically downwards when it enters a magnetic field directed to the south. What is the direction of the force on the charge? Q.12 What is the basis for saying that a current loop is a magnetic dipole? Q.13 Is it possible to increases the range of a given voltmeter? Q.14 Is it possible to increase the range of a given ammeter? Q.15 Does the magnetic field exert a force on a moving charge in the direction of the field? Q.16 Is it possible to decrease the range of a given voltmeter? Q.17 Why do we prefer phosphor-bronze alloy for the suspension wire of a moving coil galvanometer? 1

Q.18 An electron is projected into a uniform field at right angles to the field. The electron suffers deflection. How will you decide whether the given field is electric or magnetic? 0 suggests that a strong magnetic field is set up at points near a long current- I Q.19 The equation B 2 r carrying wire. Since there is a current I and a magnetic field B. why is there not a force on the wire in accordance with the equation = I ( )? Q.20 A steady current flows in the network shown in Fig 9.77. What will be the magnetic field at the center of the network? Q.21 A charged particle in a plasma trapped in a magnetic bottle leaks out after a millisecond. What is the total work done by the magnetic field during the time the particle is trapped? Q.22 A charged particle enters a uniform magnetic field at an angle of 85 0 with the magnetic lines of force. The path of the particle is a circle. Is it true or false? Q.23 There is no change in the energy of a charged particle moving in a magnetic field although a magnetic forces is acting on it. Is it true or false? Q.24 What is the resistance of an ideal voltmeter? Q.25 What is the expression for torque on a magnetic dipole placed in a uniform magnetic field? Q.26 State two factors on which the sensitivity of moving coil galvanometer depends. Q.27 What will be the path of a charged particle moving perpendicular to a uniform magnetic field? Q.28 A charge q moves with velocity at an angle θ to a magnetic field. What is the force experienced by the particle? Q.29 What is the force on a charge moving along the direction of the magnetic field? Q.30 Write down the expression for the force on a current-carrying conductor placed in a magnetic field? Q.31 Out of an ammeter and a voltmeter, which of the two has higher resistance? 2

Q.32 Why are pole-pieces of a galvanometer made concave? Q.33 State Biot-Savart s law. Q.34 A current is set up in a long copper pipe. Is there a magnetic field (a) inside (b) outside the pipe? Q.35 - Consider the circuit shown in Fig 9.78 where APB and AQB are semi-circles. What is the magnetic field at the current C of the circular loop? Q.36 What type of fields are produced by moving electron? By stationary electron? Q.37 What is the nature of magnetic field in a moving coil galvanometer? Q.38 What is the SI unit of μ0? Q.39 Write Biot-Savart s law for the magnetic field due to a current element. Q.40 In what respect does a wire carrying a current differ from a wire which carries no current? Q.41 An electron moving with a velocity of 10 7 m s -1 enters a uniform magnetic field of 1 T along a direction parallel to the field. What would be its trajectory? Q.42 A certain proton moving through a magnetic field region experiences maximum force. When does this occur? Q.43 State the principle of moving coil galvanometer. Q.44 Show the magnetic lines of force around a straight current-carrying conductor. Q.45 An air-core solenoid, having N turns, of length is carrying a current I ampere. If an iron core is inserted in it, how is its field modified? 3

Q.46 Can a cyclotron accelerate neutrons? Q.47 Write an expression for the magnetic field produced by an infinitely long straight wire carrying a current I at a short perpendicular distance a from itself. Q.48 State the rule related to the direction of current through a linear conductor and magnetic field. Q.49 A charged particle is released from rest in a region of steady and uniform electric and magnetic fields, which are parallel to each other. What will be the nature of the path followed by the charged particle? Q.50 Define current sensitivity of a moving coil galvanometer. Q.51 What is a shunt? State its SI unit. Q.52 A charge q is moving in a region where both the magnetic field and electric field are simultaneously present. What is the Lorentz force acting on the charge? Q.53 Give two factors by which the current sensitivity / voltage sensitivity of a moving coil galvanometer can be increased? Q.54 What is Lorentz magnetic force? Q.55 What is the magnetic force exerted by a magnetic field on a stationary charge? Q.56 Explain why the kinetic energy of the particle after emerging from the magnetic field remains unaltered? Q.57 What is the work done by magnetic field on a moving charge? Q.58 Write an expression for the force experienced by a charged particle moving in a uniform magnetic field B. Q.59 In the diagram below is shown a circular loop carrying current I. Show the direction of the magnetic field with the help of lines of force. Q.60 Is the source of magnetic field an analogue to the source of electric field? 4

Q.61 In a chamber of uniform magnetic field, an electron beam enters with velocity. Write the expression for the force experienced by the electrons. Q.62 An electron beam projected along + X-axis, experiences a forces, due to a magnetic field, along + Y-axis. What is the direction of the magnetic field? Q.63 A charged particle enters into a uniform magnetic field and experiences an upward force as indicated in the figure. What is the charge sign on the particle? Q.64 When is the force experienced by a moving charge in magnetic field (a) maximum (b) minimum Q.65 Under what condition does an electron moving through a magnetic field experience maximum force? Q.66 How can a moving coil galvanometer be converted into a voltmeter? Q.67 Write SI unit of magnetic field. Q.68 Write one condition under which an electric charge does not experience a force in a magnetic field. Q.69 The force experienced by a particle of charge e moving with velocity in a magnetic field is given by = e ( ). Of these, name the pair of vectors which are always at right angles to each other. Q.70 State Ampere s circuital law. Q.71 Define an ampere in terms of the force between current-carrying conductors. Q.72 State the principle of cyclotron. Q.73 Why is an ammeter always connected in series? Q.74 How can a galvanometer be converted into an ammeter? Q.75 An electron moving with velocity along + -axis enters a uniform magnetic field directed along + y-axis. What is the magnitude and direction of force on the electron? 5

SHORT ANSWER QUESTIONS Q.76 If the magnetic field is parallel to the positive y-axis and the charged particle is moving along the positive x-axis (Fig 9.83), which way would the Lorentz force be for (a) an electron (b) a proton? Q.77 What is the path of a charged particle moving in a uniform electrostatic field with initial velocity (i) parallel to the field? (ii) perpendicular to the field? (iii) at any arbitrary angle with the field direction? Q.78 A straight section AB of a circuit lies along the X-axis from = - to = + and carries a steady current I. What is the magnetic field due to the section AB at a point = + a? Q.79 Is displacement current, like conduction current, a source of magnetic field? Q.80 Suppose we set up a path of integration around a cable that contains 12 wires with different currents (some in opposite directions ) in each wire. How do we calculate current in Ampere s law in such a case? Q.81 The net charge on a current-carrying conductor is zero. Then, why does it experience a force in a magnetic field? Q.82 Is it possible to convert a galvanometer into an ammeter of range I < I g? I g is the maximum current that can be passed through the galvanometer. Q.83 A circular loop of radius R carries a current I. Another circular loop of radius r(<<r) carries a current and is placed at the centre of the larger loop. The planes of the two circles are at right angle to each other. Find the torque acting on the smaller loop. 6

Q.84 An α-particle and an electron are projected into a uniform magnetic field with the same velocity such that is perpendicular to. Compare the period of revolution of the α-particle with that of proton. Q.85 Establish the dimensional formula of B. Q.86 An α-particle moving in a straight line enters a uniform magnetic field parallel to the field direction. How will its path and velocity change? Q.87 We can use Ampere s law to derive the formula for magnetic field due to an infinitely long straight current-carrying wire. Why the same derivation is not valid for magnetic field in a plane normal to a current-carrying straight wire of finite length, and passing through the mid-point of the wire? Q.88 What is the magnetic field at the centre of a current-carrying cube made of twelve wires? Q.89 Compare Gauss s law and Ampere s law. Q.90 Apply Ampere s law qualitatively to the three parts as shown in Fig 9.85. Q.91 What do you understand by the term current element? What is its SI unit? What is the significance of current element? Q.92 Free electrons are in continuous motion in a conductor. Even then no magnetic force acts on the conductor unless a current is passed through it. Why? Q.93 Why does a solenoid contract when current is passed through it? Q.94 There is no magnetic field near a conductor in which no current is flowing. Why? Q.95 A uniform electric field and a uniform magnetic field are produced pointing in the same direction. What will happen to its velocity? Q.96 A narrow beam of charged particles of different species and speeds impinges on small hole at one end of a tube with crossed (i.e., transverse) uniform electric and magnetic fields both normal to the initial velocity direction. What can you say about the part of the beam which comes out of the other end of the tube through another small hole? Will the arrangement select out a particular species of particles? or will it select out particles with a particular speed? 7

Q.97 (a) Describe qualitatively the path of a charged particle moving in a uniform electrostatic field, with initial velocity (i) parallel to the field, (ii) perpendicular to the field, (iii) at an arbitrary angle with the field direction. (b) Describe qualitatively the path of a charged particle moving in a uniform magnetic field, with initial velocity (i) parallel to the field. (ii) perpendicular to the field, (iii) at an arbitrary angle with the field direction. (c) Describe qualitatively the path of a charged particle moving in a region with uniform electrostatic and magnetic fields parallel to each other, with initial velocity, (i) parallel, (ii) perpendicular, (iii) at an arbitrary angle with the common direction of the fields. Q.98 (a) State Ampere s law connecting the line integral of B over a closed path to the net current crossing the area bounded by the path. (b) Use Ampere s law to derive the formula for magnetic field due to an infinitely long straight currentcarrying wire. (c) Explain carefully why the same derivation as in (b) is not valid for magnetic field in a plane normal to a current-carrying straight wire of finite length, and passing through the mid-point of the wire. Q.99 If a student by mistake connects voltmeter in series with or an ammeter in parallel of a circuit, what will happen? Q.100 A neutron, a proton, an electron and an alpha particle enter a region of constant magnetic field with equal velocities. The magnetic field is along the inward normal to the plane of the paper. The tracks of the particles are labelled in Fig 9.86. Which of the tracks show the path of the electron and α-particle? Q.101 A charged particle moving in a straight line enters a uniform magnetic field at an angle of 45 0. What will be its path? Q.102 The magnetic induction inside a straight solenoid of finite length is always less than μ 0 ni. Is this statement true or false? 8

Q.103 What is the path of a charged particle moving in a uniform magnetic field with initial velocity (i) parallel to the field? (ii) perpendicular to the field? (iii) at an arbitrary angle with the field direction? Q.104 An electron is moving along a straight path in a certain region of space. Can we conclude that there is no magnetic field in the region? Q.105 What is the force that a conductor carrying a current I experiences when placed in a magnetic field? What is the direction of this force? Q.106 Draw a circuit showing how an ammeter and a voltmeter can be connected to a resistor to measure the current and voltage at a given instant. Q.107 Write the relation for force between two parallel wires carrying current and hence define unit of current. Q.108 In a certain arrangement, a proton does not get deflected while passing through a magnetic field region. Under what condition is it possible? Q.109 State any rule which relates the direction of electric current and the direction of the accompanying magnetic field. Q.110 Deduce the expression for the magnetic field produced at the centre of a semi-circular wire loop of radius R carrying a current I. Q.111 How much is the flux density B at the centre of a long solenoid? Q.112 An electron and a proton enter perpendicularly to a uniform magnetic field with the same speed. How many times larger will be the radius of the proton s path than the electron s path? Given : proton is 1840 times heavier than the electron. Q.113 A rectangular loop of area A, having N turns and carrying a current of I ampere, is held in a uniform magnetic field B. (i) What is the expression for the maximum torque experienced by the loop? (ii) In which orientation, will the loop be in stable equilibrium? Q.114 Two protons P and Q moving with the same speed enter magnetic fields B 1 and B 2 respectively at right angles to the field directions. If B 2 is greater than B 1, for which of the protons P and Q, the circular path in the magnetic field will have a smaller radius? Q.115 Give the magnitude of magnetic field at a point well inside a current-carrying solenoid? Q.116 How does (i) an ammeter (ii) a voltmeter differ from a galvanometer? 9

Q.117 A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and in the plane of the loop. If a steady current I is established in the wire as shown in Fig 9.88, what will happen to the loop? Q.118 Equal currents i are flowing through two infinitely long parallel wires. Will there be a magnetic field at a point exactly half way between the wire when the currents in them are (i) in the same direction (ii) in the opposite direction. Q.119 How will the magnetic field intensity at the centre of a circular coil carrying current change, if the current through the coil is doubled and the radius of the coil is halved? Q.120 The energy of a charged particle moving in a uniform magnetic field does not change. Why? Explain. Q.121 An electron is moving along a straight path in a certain region of space. Can we conclude that there is no magnetic field in the region? Q.122 Name the rule which gives the direction of the force on a current-carrying conductor placed in a uniform magnetic field. Write the condition for which this force will have (i) maximum (ii) minimum value. Q.123 What is a solenoid? Comment on the magnetic field around a solenoid. Q.124 State Fleming s left hand rule. Q.125 Two wires of equal lengths are bent in the form of two loops. One of the loops is square-shaped whereas the other loop is circular. These are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience greater torque? Give reasons. Q.126 An electron and a proton, moving parallel to each other in the same direction with equal momenta, enter a uniform magnetic field which is at right angles to their velocities. Trace their trajectories in the magnetic field. Q,127 A charge 8 C is moving with velocity = ( ˆ7 + 4 ˆK ) in a magnetic field = ( ˆ7 + 4 ˆK ) Wbm -2. Find the force acting on the charge. 10

Q.128 Write two uses of cyclotron. Q.129 Which one of the two, an ammeter or a milli-ammeter, has a higher resistance and why? Q.130 When a voltmeter is put across a part of the circuit, does it read slightly less or more than the original voltage drop across that part? Explain. Q.131 Sketch the magnetic field lines for a finite solenoid. Explain why the field at the exterior mid-point is weak while at the interior it is uniform and strong. Q.132 State two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer. Q.133 Compare a voltmeter and an ammeter. SHORT ANSWER QUESTIONS Q.134 What is the magnetic field at the common center O of two concentric coils of radii r 1 and r 2 shown in Fig 9.91 (i) and (ii)? Current in each coil is I. Q.135 Fig 9.92 shows a circular coil joined to two semi-infinite long conductors. What is the magnetic field induction at the center of the coil? 11

Q.136 A current I flows along a thin wire shaped as shown in Fig 9.93. The radius of a curved part of the wire is R. The angle subtended at O by the straight part is 2Ø. What is the magnetic field induction at O? Q.137 Determine the magnetic field at C in Fig 9.95 Q.138 Fig 9.96 show two concentric coils, each of radius r, inclined to each other at 90 0. 1 and 2 are the magnetic field inductions due to coils, each carrying current I. What is the magnitude of the net magnetic field at the common center C of the two coils? 12

Q.139 Three semi-infinite long wires are along x, y and z-axes. Same current I flows in the three wires as shown in field at the point P (0, 0, a). Q.140 An electric current I is flowing through an infinitely long conductor bent into a loop of the shape as shown in Fig 9.98. Find the magnitude and direction of magnetic field at the centre O of the circular part of the loop. Q.141 Determine the magnetic field induction at O due to the current-carrying conductor in Fig 9.99. Q.142 Fig 9.100 shows two mutually perpendicular conductors. Find the equation of locus of zero magnetic field points. 13

Q.143 A U-tube of uniform square cross-section of sides a contains mercury of density ρ. Electrodes are sealed inside the upper and lower sides of the horizontal bottom part of the U-tube and a current of strength I is passed through the mercury vertically. A magnetic field of induction B acts horizontally at right angles to the current. What is the difference in mercury levels? Q.144 How does the interaction of a magnetic field with a charged particle differ from the interaction of an electric field with a charged particle? Q.145 Answer the following questions : (a) A cloud chamber photograph shows a pair of circular tracks emerging from a common point. The tracks have similar density of droplets but curve in opposite directions in a plane normal to the magnetic field maintained in the chamber. If one of the ionizing particles is established to be an electron guess the high energy event that took place at the common point of the tracks. (b) A similar event as in (a) photographed in a liquid-hydrogen bubble chamber shows spiral tracks instead of circular tracks. Explain why? Q.146 An electron and a proton are moving along the same direction with the same kinetic energy. When they pass through a uniform magnetic field perpendicular to the direction of their motion, they describe paths of the same radius. Is this statement true or false? 14

Q.147 A wire ABCDEF (with each side of length L) bent as shown in Fig 9.102 and carrying a current I is placed in a uniform magnetic induction B parallel to the positive Y-direction. The force experienced by the wire is..in the...direction. Q.148 A galvanometer has a resistance of 50 ohm. A resistance of 1 Ω is connected across its terminals. What part of the total current will flow through the galvanometer? Q.149 Why is a voltmeter always connected in parallel with a circuit element across which voltage is to be measured? Q.150 A straight wire carrying a current of 12 A is bent into a semi-circular are of radius 0.02 m as shown in Fig 9.103 (a). What is the direction and magnitude of at the centre of the are? Would answer be different if the wire were bent into a semi-circular are of the same radius but in the opposite way as shown in Fig 9.103 (b)? Q.151 A wire of length L is wound on a spherical form, and a current I is passed through it. The coil is then placed in a uniform magnetic field of induction B. How many turns should it have for the torque on it to be maximum? What is the value of this torque? Q.152 A proton and an alpha particle having the same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to their direction of motion. Compare the radii of the paths of proton and alpha particle. 15

Q.153 A proton and an alpha particle enter a uniform magnetic field perpendicularly with the same speed. How many times is the time period of the -particle more than that of the proton? Deduce an expression for the ratio of the radii of the circular paths of the two particles. Q.154 A charge q moving in a straight line is accelerated by a potential difference V. It enters an uniform magnetic field B perpendicular to its path. Deduce in terms of V an expression for the radius of the circular path in which it travels. Q.155 A particle with charge q moving with velocity in the plans of paper enters a uniform magnetic field B acting perpendicular to the plane of the paper. Deduce an expression for the time period of the charge as it moves in a circular path in the field. Why does the kinetic energy of the charge not change, while moving in the magnetic field? Q.156 A proton, deuteron and an alpha particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. Compare the radii of their circular paths. Q.157 An α-particle and a proton are accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature. Q.158 A cyclotron s oscillator frequency is 10 MHz. What should be the operating magnetic field for acceleration protons? If the radius of its Dees is 0.60 m, what is the kinetic energy of the proton beam produced by the accelerator? (e = 1.6 10-9 C, m p = 1.67 10-27 kg) Express your answer in units of MeV. (1 MeV = 1.602 10-13 J). Q.159 A rectangular loop of sides 0.25 m and 0.10 m carrying a current of 15 A with its longer side parallel to a long straight conductor 0.02 m apart carrying a current of 25 A. What is the net force on the loop? Q.160 Two parallel wires carrying current in the same direction attract each other while two beams of electrons travelling in the same direction repel each other. Explain why. Q.161 (a) A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself, i.e., turns about the vertical axis? (b) A current-carrying circular loop is located in a uniform external magnetic field. If the loop is free to turn, what is its orientation, of stable equilibrium? Show that in this orientation, the flux of the total field (external field + field produced by the loop) is maximum. (C) When a loop of irregular shape, made of flexible wire, is placed in a magnetic field, it assumes a circular shape. Why? CONCEPTUAL PROBLEMS Q.162 How many ways are there to produce a magnetic field? 16

Q.163 Why the earth s magnetic field does not affect the working of a moving coil galvanometer? Q.164 A current-carrying wire placed parallel to magnetic field does not tend to rotate. What conclusion do you draw from this? Q.165 A current is sent through a vertical spring from whose lower end a weight is hanging. What will happen? Q.166 Wires that carry equal but opposite currents are often twisted together to reduce their magnetic effect at distant points. Why is this effective? Q.167 A liquid hydrogen bubble chamber photograph shows a pair spiral tracks emerging from a common point. The tracks curve in opposite directions in a plane normal to the magnetic field maintained in the chamber. Explain why spiral paths are observed. Q.168 Is constant in magnitude for points that lie on a given line of induction? Q.169 A charged particle is projected with velocity in a uniform magnetic field at an angle θ (0 0 < θ < 90 0 ). What will be the path of the charged particle? Justify your answer. Q.170 State a rule with the help of which we can determine the polarity of a solenoid. Q.171 Fig 9.106 shows an electron beam which is first diverging and then converging. Guess a possible explanation for this situation. Also guess the nature of the shaded strip. Q.172 Refer to the use of Ampere s law to derive the formula for magnetic field due to an infinitely long straight current-carrying wire. Why the same derivation is not valid for magnetic field in a plane normal to a current-carrying straight wire of finite length and passing through the mid-point of the wire. Q.173 No net force acts on a rectangular coil carrying a steady current when suspended freely in a uniform magnetic field. Is it true or false? Q.174 In the formula X=3YZ 2, the quantities X and Z have the dimensions of Y in the MKSQ system are (Fill in the blank). 17

Q.175 An electron beam is moving vertically downwards. If it passes through a magnetic field which is directed from south to north in a horizontal plane, then in which direction the beam would be deflected? Q.176 A metallic block carrying current I is subjected to a uniform magnetic induction as shown. The moving charges experience a force given by.which results in the lowering of the potential of the face..assume the speed of the carriers to be v. Fill in the blanks. Q.177 A loop, of irregular shape, carrying current is located in an external magnetic field. What shall happen if the wire is flexible? Q.178 What is a radial magnetic field? Q.179 Why a cyclotron is not suitable to accelerate electrons? Q.180 What are the two advantages of soft iron core used in moving coil galvanometer? LONG ANSWER QUESTIONS Q.181 With the help of a neat and labelled diagram, explain the underlying principle and working of a moving coil galvanometer. 18

Q.182 Derive a mathematical expression for the force per unit length experienced by each of the two long current carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in the opposite direction kept near each other in air repel? Q.183 Draw a neat and labelled diagram of a cyclotron. State the underlying principle and explain how a positively charged particle gets accelerated in this machine. Show mathematically that the cyclotron frequency does not depend upon the speed of the particle. Q.184 State the Biot-Savart law for the magnetic field due to a current-carrying element. Use this law to obtain a formula for magnetic field at the centre of a circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for a current loop clearly indicating the direction of the field. Q.185 Discuss the motion of a charged particle moving in a direction making an angle θ with the direction of the uniform magnetic field. Q.186 What is an ammeter? How can a galvanometer be converted into an ammeter? Explain Q.187 Derive an expression for the maximum force experienced by a straight conductor of length, carrying current I and kept in a uniform magetic field B. Q.188 Using Biot-Savart law, derive the expression for the magnetic field at a distance along the axis from the centre of a current-carrying circular loop. Q.189 Derive an expression for the magnetic field along the axis of an air-cored solenoid, using Ampere s circuital law. Q.190 Explain with the help of a labelled diagram the working principle of a cyclotron. Show that the cyclotron frequency does not depend on the speed of the particle. Write one of the uses and point out one of the drawbacks of a cyclotron. Q.191 Explain Biot-Savart law for a small current-carrying conductor and using this law, derive an expression for the magnetic field at the centre of a current-carrying circular coil. Q.192 Explain with the help of a labelled diagram, the principle and construction of a cyclotron. Deduce an expression for the cyclotron frequency and show that it does not depend on the speed of the charged particle. 19