CURRENT-CARRYING CONDUCTORS / MOVING CHARGES / CHARGED PARTICLES IN CIRCULAR ORBITS

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Geraldine Collins
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PHYSICS A2 UNIT 4 SECTION 4: MAGNETIC FIELDS CURRENT-CARRYING CONDUCTORS / MOVING CHARGES / CHARGED PARTICLES IN CIRCULAR ORBITS # Questions MAGNETIC FLUX DENSITY 1 What is a magnetic field?

In a magnetic field, a force is exerted on magnetic or magnetically susceptible materials 3 How can magnetic fields be represented?

6 What are the field lines between a North and South pole of two magnets? 7 What are the field lines between two North poles of two magnets? 8 What is created when a current flows in a wire?

1 PHYSICS A2 UNIT 4 SECTION 4: MAGNETIC FIELDS CURRENT-CARRYING CONDUCTORS / MOVING CHARGES / CHARGED PARTICLES IN CIRCULAR ORBITS # Questions MAGNETIC FLUX DENSITY 1 What is a magnetic field? A region in which a force acts 2 What is a force exerted on in a magnetic field? In a magnetic field, a force is exerted on magnetic or magnetically susceptible materials 3 How can magnetic fields be represented? By field lines 4 In which direction do magnetic field lines travel? Magnetic lines travel from North to South 5 What are the field lines around a North/South bar magnet? 6 What are the field lines between a North and South pole of two magnets? 7 What are the field lines between two North poles of two magnets? 8 What is created when a current flows in a wire? When a current flows through a wire, a magnetic field is induced around the wire 9 What are the field lines around a current flowing through a wire? The field lines are concentric circles centred on the wire 10 How may you work out the direction of the magnetic field around a current-carrying wire? Using the right-hand grip rule Curl your right hand into a fist and stick up your thumb

Point your thumb in the direction of the current through the wire Your fingers will then curl in the direction of the field 11 What is the field pattern around one coil of wire?

The shape is called a solenoid 13 What happens when you put a current-carrying wire into an external magnetic field?

2 Point your thumb in the direction of the current through the wire Your fingers will then curl in the direction of the field 11 What is the field pattern around one coil of wire? A wire going into the board is represented by an X cross A wire coming out of the board is represented by a point 12 What is the field pattern around many coils of wires? What is this shape called? The shape is called a solenoid 13 What happens when you put a current-carrying wire into an external magnetic field? A current-carrying wire placed at a non-zero angle to the lines of force of a magnetic field experiences a force on the wire due to the field This effect is known as the motor force The force is perpendicular to the lines of force 14 Where will the force act if the current is parallel to the field lines? If the current is parallel to the field lines, no force acts 15 What is Fleming s Left Hand Rule used to predict? Used to predict the direction of the force experienced by the wire when its perpendicular to the field lines of the magnetic field 16 What does each finger represent in Fleming s Left Hand Rule? First finger is direction of the uniform magnetic field The second finger is the direction of convectional current Thumb is the direction of the force (the direction of motion) 17 What happens if an A.C. is passed through the wire in a magnetic field? If an alternating current is passes through the wire, the direction of the current is constantly reversed According to Fleming s Left Hand Rule, when the current is reversed, the direction of the force on the wire is reversed This will make it move in the opposite direction And hence the wire will be made to vibrate, as its direction is constantly changed 18 In which direction does conventional current flow? From positive to negative The direction that a positive charge would flow 19 Under what conditions in the force on a current-carrying wire proportional to the strength of the magnetic field? When the direction of the current (the wire) is placed at 90 o (perpendicular) to the direction of magnetic field lines 20 What is the Magnetic Flux Density? The magnetic field strength is called the magnetic flux density, B 21 What is the definition of Magnetic Flux Density?

The force on one metre of wire carrying a current of one ampere at right angles to the magnetic field 22 What are the units of Magnetic Flux Density?

3 The force on one metre of wire carrying a current of one ampere at right angles to the magnetic field 22 What are the units of Magnetic Flux Density? The Tesla (T) equal to 1Nm -1 A -1 1 Tesla = 1 " 23 Is Magnetic Flux Density a vector or a scalar value? Vector 24 What is the size of the force, F, on a current-carrying wire proportional to and under what conditions? The size of the force F is proportional to the current, I, the length of the wire, l, and the magnetic flux density, B when the wire is at right angles to the magnetic field 25 Hence what is the equation for the Force on a current-carrying wire? Hence, F = BIl 26 What if the wire isn t at right angles to the magnetic field? If the wire isn t at right angles to the magnetic field, then it will still experience a force, but it will be smaller Hence, F = BIl 27 Explain how a couple is formed on a coil in a magnetic field Consider a rectangular current-carrying coil in a uniform horizontal magnetic field The coil has n turns of wire and can rotate about a vertical axis The long sides of the coil are vertical Each wire down each long side experiences a force BIl Each long side therefore experiences a horizontal force F = (BIl)n in opposite directions at right angles to the field lines The pair of forces acting on the long sides (XW and YZ) form a couple as the forces are not directed along the same line The torque in a couple = Fd where d is the perpendicular distance between the line of action of the forces on each side If the plane of the coil is at an angle a to the field lines, then d = wcos(a) where w is the width of the coil Therefore, the torque = Fwcosa = BIlnwcosa FORCES ON CHARGED PARTICLES 28 What acts on charged particles moving in a magnetic field? What does this explain? A force acts on charged particles moving in a magnetic field This is why a current-carrying wire experiences a force in a magnetic field electric current in a wire is the flow of negatively charged electrons 29 How does F = BIl link to particles? The force on a current-carrying wire in a magnetic field perpendicular to the current is given by F = BIl Current, I, is the flow of charge, Q, per unit time So I = A charged particle which moved with a distance L in time t has a velocity, v = "#$%&'( "#$ =

4 So l = vt 30 How does F = BIl give F = BQv? Hence, if F = BIl and l = vt and I = Then F = B vt The t s then cancel to give F = BQv 31 Under what conditions does F = BQv? F = BQv gives the force on a single charged particle moving through a magnetic field, where its velocity is perpendicular to the magnetic field 32 How does the magnetic field of a particle link to circular motion? Charged particles in a magnetic field are deflected in a circular path By Fleming s left hand rule, the force on a moving charge in a magnetic field is always perpendicular to its direction of travel This is the condition for circular motion 32.1 How can you find the direction of the force of single charged particles? Fleming s left-hand rule to find the direction of force for a positively charged particle Then either point your finger in the opposite direction or use your right hand normally to find the direction of force for a negative charge 32.2 Is work done by the magnetic field on the particle? No because the force always acts at right angles to the velocity of the particle Its direction of motion is changed by the force, but not its speed The kinetic energy of the particle is unchanged by the magnetic field And since there is no change in energy, there is no work done 33 What is the equation for the radius of curvature of a particle s path and how is it derived? The radius, r, of the circular orbit of a charged particle depends on the speed v, of the particles and the magnetic flux density B At any point on the orbit, the particle is acted on by a magnetic force F = BQv And it experiences a force due to centripetal acceleration F = Therefore, BQv = Rearranging this equation for r gives r = " " 34 Hence, what happens to the strength of the magnetic field as the radius of curvature increases/decreases? Strength of the magnetic field is B Hence, is r is increased, B is decreased And if r is decreased, B is increased 35 How can you get the frequency of rotation in terms of B, Q and m? The frequency of rotation for an object in circular motion is given by its velocity v divided by the distance it travels in each rotation 2πr speed = "#$%&'( "#$ Therefore, time = "#$%&'( = " = T "##$ But f = And so f = " Substituting r = " into this gives f = " "( " = " " ) " 36 Hence, how does the velocity of a particle affect the frequency of its rotation? So the velocity of rotational of a charged particle in a magnetic field is independent of its

5 velocity 37 What does the time it takes particles to complete a full circle depend on? The time taken to complete a full circle depends only on the magnetic flux density, and its mass and charge Increasing a particle s velocity will make it follow a circular path with a larger radius, but it will take the same time to complete it 37.1 What effect does increasing the particle s velocity have? Increasing a particle s velocity will make it follow a circular path with a larger radius, but it will take the same time to complete it 38 What are cyclotrons? An apparatus in which charged atomic and subatomic particles are accelerated by an alternating electric field while following an outward spiral or circular path in a magnetic field 39 What can cyclotrons are used to produce? Used to produce radioactive tracers or high-energy beams of radiation for use in radiotherapy 40 What is the basic structure of a cyclotron? A cyclotron is made up of two hollow semi-circular electrodes with a uniform magnetic field applied perpendicular to the plane of the electrodes, and an alternating potential difference between the electrodes 41 How does a cyclotron increase the speed of the particle? Charged particles are produced and fired into one of the electrodes, where the magnetic field makes them follow a (semi)circular path and then leave the electrode An applied potential difference between the electrodes then accelerates the particles across the gap So that the particles enter the next electrode with a higher speed Because of this higher speed, the particle will follow a circular path with a larger radius (r = " " ) Before leaving again At this point, the direction of the potential difference between the electrodes is reversed and so the particle is accelerated again before entering the next electrode This process repeats as the particle spirals outwards, increasing its speed, before eventually leaving the cyclotron 42 What power supply does a cyclotron use? Alternating current 43 What is a mass spectrometer? Used to analyse different types of atoms present in a sample The atoms of the sample are ionised and directed in a narrow beam at the same velocity into a uniform magnetic field Each is deflected in a semi-circle path by the magnetic field onto a detector Where it induced a current and so relative abundances can be measured and compared 44 How can you change the path of a particle in a mass spectrometer? The radius of curvature of the path of each ion depends on the specific charge of the particle This is because r = " where the velocity and magnetic field density are constant " ELECTROMAGNETIC INDUCTION 45 What is electromagnetic induction? If a conducting rod moves through a magnetic field, its electrons will experience a force Which means that they will accumulate at one end of the rod This creates a positive charge at one end of the rod compared with the negative charge at the other end of the rod à this is a potential difference Hence, an e.m.f. is induced across the rod If the rod is part of a complete circuit, then an induced current will flow through it, this is called electromagnetic induction 46 How is an e.m.f. induced across a straight conductor moving through a magnetic

6 field? An e.m.f is induced when there is relative motion between a conductor and a magnet The conductor can move and the magnetic field stay still or the other way round Either way, you get an e.m.f. Flux cutting (i.e. moving a conductor through a magnetic field) will always induce an e.m.f but will only induce a current if the circuit is complete 47 What is magnetic flux? The product of the magnetic flux density B and the area over which it is applied A is called the magnetic flux Φ 48 What is magnetic flux measured in? webers Wb 49 What is the equation for magnetic flux? The total magnetic flux Φ passing through an area, A, normal (perpendicular) to a magnetic field, B, is given by: Φ = BA 50 Under what conditions does the equation for magnetic flux apply? When the magnetic field is perpendicular to the area through which it acts 51 What is flux linkage? The product of the magnetic flux passing through the coil Φ, and the number of turns on the coil cutting the flux N is called the flux linkage 52 What is flux linkage measured in? Measured in weber turns Wb.turns 53 What are the two equations for flux linkage? Flux linkage = ΦN = BAN 54 What is the flux linkage if the wire coil is parallel to the flux density? There is no flux linkage if the wire coil is parallel to the flux density 55 What is the equation for the flux linkage if the wire coil is at an angle to the flux density? The maximum flux linkage is when the flux density is at right angles to the wire The minimum flux linkage is when the flux density is parallel to the wire Hence, the flux linkage increases from zero to maximum as the wire turns from parallel to normal Φ = BANcosθ Hence Flux linkage = ΦN = BANcosθ 56 At what angle is the flux linkage the maximum? When the flux density is at right angles (perpendicular) to the wire Hence when cosθ=1 and θ = 0 57 What is Faraday s Law? Faraday s Law states that the induced e.m.f in a circuit is equal to the rate of change of flux linkage through the circuit 58 What is the equation for Faraday s Law? e.m.f = ε = N Where N is the change of flux linkage per second 59 What is the gradient of a graph of Nϕ against time? Since ε = N The gradient of the graph represents the e.m.f

7 60 What is the area under the graph of e.m.f against time? Since ε = N The area under the graph represents NΦ aka the flux linkage 59.1 What is an equation for the e.m.f produced by a conducting rod moving through a uniform magnetic field? To use Faraday s Law of ε = N, you must know the amount of flux that the rod cuts through in time t Flux Φ is given by BA, so you need to find A Area is the distance travelled in a time t distance = velocity x time = v t Hence, the area that the flux cuts in this time is given by lv t Φ = BA, so Φ = Blv t Therefore for one turn, e.m.f, ε = N, = "# = Blv 61 What is Lenz s Law? The induced e.m.f is always in such a direction as to oppose the change that caused it 62 What can Lenz s Law be used to find? Be used to find the direction of the induced e.m.f and current in a conductor travelling at right angles to a magnetic field 63 Why does the induced force cause resistance in a conductor moving down through a magnetic field? The idea that an induced e.m.f will oppose the change that caused it agrees with the principle of the conservation of energy The energy used to pull a conductor through a magnetic field, against the resistance caused by magnetic attraction, is what produces the induced current 64 How is an e.m.f. induced in a rotating coil? When a coil rotates uniformly (at a steady speed) in a magnetic field, the coil cuts the flux and an alternating e.m.f is induces The amount of flux cut by the coil (flux linkage) is given by NΦ = BANcosθ As the coil rotates, θ changes, so the flux linkage varies sinusoidally between + BAN and - BAN 65 What does the speed that θ changes depend on? How fast θ changes depends on the angular speed, ω, of the coil θ = ωt 66 Hence, what is the equation for flux linkage in a rotating coil? NΦ = BANcosωt 67 What does the induced e.m.f depend on? The e.m.f depends on the rate of change of flux linkage, so it also varies sinusoidally 68 What is the equation for the induced e.m.f in a rotating coil? ε = BANωsinωt 69 What would the graph of flux linkage against time look like for a rotating coil? 70 When is the flux linkage the maximum for a rotating coil? Flux linkage is maximum at 0 o, and 180 o

8 Hence when T=0 and T=1 71 What would the graph of e.m.f. against time look like for a rotating coil? 72 When would the e.m.f be the maximum for a rotating coil? E.m.f maximum at 90 o, 270 o 73 What are 4 ways to increase the e.m.f produced? 1) Increasing the speed of rotation will increase the frequency and increase the maximum e.m.f 2) Increasing the magnetic flux density, B, will increase the maximum e.m.f (but will have no effect on the frequency) 3) Increasing the number of turns of the coil will increase the e.m.f 4) Increasing the cross sectional area A of the coil 74 What will happen to the peak voltage and time period if the frequency is halved? If the frequency is halves, the time period is doubled, and so the peak voltage is halved 75 What will happen to the peak voltage and time period if the frequency is doubled? If the frequency is doubled, the time period is halves and the peak voltage is doubled 76 Why does a magnet moving down a metal tube move more slowly? The magnetic field lines (flux density) are around the metal tube Hence, a magnet falling through them is cutting them at right angles Because of this, the magnet induces a current in the metal tube This, in turn, produces a magnetic field The direction of this current then opposes the change in the magnetic field Resulting in the magnet being repelled upwards and so falls more slowly 77 How is an e.m.f generated in flux cutting? An e.m.f is induced in a conductor provided the conductor cuts the lines of a magnetic field The direction of the conductor is at right angles to the field lines The magnitude of the induced e.m.f ε = Blv 78 How does a fixed coil in a changing magnetic field induce an e.m.f? A small coil on the axis of a current-carrying solenoid The magnetic field of the solenoid passes the small coil If the current in the solenoid changes, an e.m.f is induced in the small coil This is because the magnetic field through the coil changes so the flux linkage through it changes, causing an induced e.m.f The flux linkage through the coil, NΦ = BAN where A is the coil area and N is the number of turns in the coil Suppose the magnetic flux density changes from B to B + B in time t So the flux linkages changes by an amount N φ = BAN Magnitude of the induced e.m.f = = " 80 How does a dynamo generate an electric current? Generators, or dynamos, convert kinetic energy into electrical energy they induce an electric current by rotating a coil in a magnetic field A generator of alternating current has slip rings and brushes to connect the coil to an external circuit The output voltage and current change direction with every half rotation of the coil, producing an alternating current 81 What is the back e.m.f? An e.m.f is induced in the spinning coil of an electric motor because the flux linkage through

9 the coil changes The induced e.m.f is referred to as back e.m.f because it acts against the p.d applied to the motor in accordance with Lenz s Law 82 What does V ε = IR mean for the spinning coil of an electric motor? At any instance, V ε = IR, where I is the current through the motor coil and R is the resistance Because the induced e.m.f is proportional to the speed of the rotation of the motor, the current changes as the motor speed changes At a low speed, the current is high because the induced e.m.f (and therefore resistance) is small At high speeds, the current is low, because the induced e.m.f (and therefore resistance) is high 83 What does multiplying V ε = IR through I give? Multiplying the equation V ε = IR by I throughout gives IV Iε = I R Rearranging this gives: IV = Iε + I R Electrical power supplied by the source = electrical power transferred to mechanical power + electrical power wasted due to circuit resistance TRANSFORMERS 84 What are transformers? Transformers are devices that make use of electromagnetic induction to change the size of a voltage for an alternating current 85 How do transformers work? An alternating current flowing in the first (primary) coil causes the core to magnetise and demagnetise continuously in opposite directions This produces a rapidly changing magnetic flux across the core Because of this, a magnetically soft material is needed This is usually iron or a special alloy The rapidly changing magnetic flux in the iron core passes through the secondary (output) coil, where it induces an alternating voltage of the same frequency, but with a different voltage, assuming the number of turns is different From Faraday s Law, the voltage in the primary and the secondary coil can be calculated from = 86 How is the equation N s = V s derived? N p V p Primary coil: V = N Secondary coil: V = N These can be rearranged to give = and = Because we assume that is a constant, then = Rearranging this gives = 87 What is a step up transformer? Increase the voltage by having more turns on the secondary coil than the primary 88 What is a step down transformer? Reduce the voltage by having fewer turns on the secondary coil 89 Why can transformers not be 100% efficient? Slight loss of energy in the form of heat 90 What can be done to make transformers more efficient? 1) low resistance windings to reduce the power wasted due to the heating effect of the current

10 2) A laminated core which consists of layers of iron separated by layers of an insulator This reduces the effect of eddy currents and keeps the magnetic flux as high as possible 3) A soft iron core, which is easily magnetised and demagnetised. This reduces power wasted through repeated magnetisation and demagnetisation of the core 91 What are eddy currents? Eddy currents are induced currents in the core itself 92 How would you calculate the efficiency of a transformer? "#$% "#$%"&'(#" " "#$%&'() "#$ "#$% "##$%&' " "#$%"& "#$ = x 100% 93 In a step-up transformer, what happens to the current? If the voltage is stepped up, the current is stepped down 94 In a step-down transformer, what happens to the current? If the voltage is stepped down, the current is stepped up 95 What is the National Grid? A network of transformers and cables, underground and on pylons, which covers all regions of the U.K to deliver electricity 96 What kind of current does the National Grid generate? Alternating current 97 What is the precise frequency of the current in the National Grid? 50Hz 98 What is the voltage produced by the National Grid? 25kV 99 Why is electricity sent around the country at a low current? The reason is that the current needed to deliver a certain amount of power is reduced if the voltage is increased So power wasted due to the heating effect of the current through the cables is reduced To deliver power, P, at voltage V, the current required I = If the resistance of the cables is R, the power wasted in the cables is I R = 100 What is the energy loss proportional to in sending electricity around the country? Power loss is proportional to I R 101 Why is the voltage stepped up for transmission through the National Grid? Therefore the higher the voltage is, the smaller the ratio of waster power to the power transmitted The more efficient the network 102 What is the voltage stepped up to for transmission through the National Grid? 400kV or more 103 Why is the voltage stepped back down for use in the home? Because high voltages raise safety and insulation issues 104 What is the voltage stepped back down to for use in the home? 230V

FXA 2008 Φ = BA. Candidates should be able to : Define magnetic flux. Define the weber (Wb). Select and use the equation for magnetic flux :

FXA 2008 Φ = BA. Candidates should be able to : Define magnetic flux. Define the weber (Wb). Select and use the equation for magnetic flux : 1 Candidates should be able to : Define magnetic flux. Define the weber (Wb). Select and use the equation for magnetic flux : Φ = BAcosθ MAGNETIC FLUX (Φ) As we have already stated, a magnetic field is