Electromagnetic induction

The diagram shows a section through the components of a speedometer for a bicycle. The front wheel axle of the bicycle is connected to a cable. The cable rotates as the bicycle wheel rotates. The other end of the cable is connected to a magnet which also rotates, as shown.

An aluminium disc is shaped so that it is close to, but not touching, the magnet. The disc is connected to a pointer by a shaft. A spring prevents the disc and shaft from freely rotating.

*(a) Explain why the aluminium disc rotates in the same direction as the magnet.

The road speed of the bicycle should be displayed by the speedometer.

Explain why the displayed speed can not be accurate, as bicycles can have different wheel diameters.

Regenerative braking supplies a current back to the power transmission system whilst slowing a vehicle. The arrangement shown can be used as a regenerative braking system on a train.

The coil rotates with the wheels of the train. Two copper rings are connected to the ends of the coil. The rings rotate with the coil and two carbon blocks make electrical contact with the rings as they rotate.

Describe how this arrangement can be used as a regenerative brake.

A specification for a new train states that the train should be able to accelerate to a speed of 360 km hour⁻¹ from rest, and that this acceleration should be completed within 40 km of level track.

The graph shows the performance of the train on a test run.

Calculate the acceleration of the train as it accelerates to a speed of

Deduce whether the performance of the train met the specification on this test run.

On curved tracks there is a maximum safe speed for the train.

Explain why there is a maximum safe speed for a train travelling on a curved track.

When the train travels at 200 km hour⁻¹, the minimum safe radius of curvature of the track is 1800 m.

Calculate the minimum safe radius of curvature for a speed of 360 km hour⁻¹.

An induction hob consists of a coil beneath a sheet of ceramic material. The coil is connected to an alternating current (a.c.) supply as shown.

pan

A steel pan containing water is placed on the induction hob.

Explain why the pan becomes hot when the supply is switched on.

The a.c. supply to the coil in an induction hob has a much higher frequency than normal mains frequency.

Explain why this is an advantage in this case.

A device called a clutch can be used to connect a motor to a load. The diagram shows a design called an eddy current clutch.

Several magnets are embedded in the plastic disc and it is rotated by the motor.

Explain why a current is induced in the copper disc when the motor is switched on.

Explain, using Lenz’s law, why the copper disc rotates.

The motor rotates at 500 revolutions per minute.

Calculate the angular speed ω of the motor.

The table shows how the turning effect exerted on a load varies with ω for a particular distance between the copper disc and the plastic disc.

Explain the trend shown by the data.

*5 The diagram shows a ‘shaker torch’. When the torch is shaken, a strong magnet moves forwards and backwards through a copper coil, powering a light-emitting diode (LED).

Each time the magnet moves through the coil a current pulse is generated. The coil is connected to a capacitor via a diode, as shown.

Once the torch has been shaken for a few minutes the switch is closed and the LED lights for a short while.

Explain how the shaker torch is able to light the LED.

The diagrams show the plan view and side view of a moving coil ammeter.

The fixed soft iron cylinder and magnets produce a uniform magnetic field of magnetic flux density B. The coil is able to rotate within this magnetic field. The coil has width w and length l. There is a current I in the coil in the direction shown in the side view diagram.

Explain which way the coil will rotate.

Show that the moment M on the coil about the pivot, due to the magnetic field, is given by

M = BAIN

where A is the cross-sectional area of the coil N is the number of turns of wire on the coil.

An ammeter of this type has a resistance of 625 Ω and will measure a maximum current of 1.6 mA.

The ammeter can be adapted to measure potential difference by adding a resistor in series with the ammeter. This resistor is known as a multiplier.

The ammeter is adapted so that it can measure potential differences up to 5.0 V as shown.

The following multipliers are available:

200 Ω 2500 Ω 3125 Ω 3750 Ω

Deduce which multiplier should be used.

The coil within a very sensitive moving coil ammeter can be damaged when the ammeter is transported. The two ends of the coil are connected together when the ammeter is transported. This reduces the movement of the coil and makes it less likely to be damaged.

A student suggests that this is due to Faraday’s law and Lenz’s law.

Explain how these laws apply to this situation.

Hybrid electric vehicles (HEV) use the same device both as a generator to charge the car battery and as an electric motor to support the propulsion system. A simplified diagram of the device is shown. The coil can rotate freely around the axis.

*(a) Describe how the device can be used as both a generator and an electric motor.

The circuit diagram shows a car battery connected to an electric motor for a HEV. The battery has an electromotive force (e.m.f.) 180 V and internal resistance 0.036 Ω.

The motor has a maximum power of 88 kW.

Show that the current I drawn by the electric motor when operating at this power would be given by the equation

Solving the equation above produces an answer of I = 550 A. At maximum power, the car can accelerate from rest to sixty miles per hour in under 7 s.

The maximum charge capacity of the battery within this HEV is 6.1 amp-hour.

Deduce whether the battery could maintain this current for up to 7 s.

Hybrid electric vehicles (HEV) use the same device both as a generator to charge the car battery and as an electric motor to support the propulsion system. A simplified diagram of the device is shown. The coil can rotate freely around the axis.

*(a) Describe how the device can be used as both a generator and an electric motor.

The circuit diagram shows a car battery connected to an electric motor for a HEV. The battery has an electromotive force (e.m.f.) 180 V and internal resistance 0.036 Ω.

The motor has a maximum power of 88 kW.

Show that the current I drawn by the electric motor when operating at this power would be given by the equation

Solving the equation above produces an answer of I = 550 A. At maximum power, the car can accelerate from rest to sixty miles per hour in under 7 s.

The maximum charge capacity of the battery within this HEV is 6.1 amp-hour.

Deduce whether the battery could maintain this current for up to 7 s.

* 12 A simple electric motor consists of a coil that is free to rotate in a magnetic field.

A student connects the motor to an ammeter and a battery.

The graph shows how the current I in the coil varies with time t. The switch is closed at time T.

Explain why the current rises to a maximum then decreases. Your answer should include a reference to Faraday and Lenz’s laws.

The Shanghai Maglev Train is the first commercially operated high-speed magnetic levitation train in the world, connecting the airport and central Shanghai.

The total distance travelled is 29.9 km and the total journey time is 440 s. The train starts from rest and reaches a speed of 97 m s⁻¹ in 120 s.

Calculate the average acceleration of the train during the first 120 s.

Calculate the average speed of the train for the period following the 120 s acceleration.

Electromagnetic forces enable the train to levitate above a steel rail.

Explain why magnetic levitation is an advantage for a high-speed transport system.

*(c) A linear induction motor provides the force to accelerate the train forwards. A current flows in sequence through coils of wire mounted in the track. The train is dragged along as the magnetic field progresses along the coils of wire in the track. This is similar to moving a permanent magnetic field away from a conductor.

A teacher demonstrates this effect by quickly removing one end of a bar magnet from a suspended aluminum ring.

When the magnet is removed from the ring, the ring moves in the same direction as the magnet.

Explain, using the laws of electromagnetic induction, why the ring moves in the direction of the magnet.

A circuit is set up as shown in the diagram. Lamps X and Y are identical. The coil has a soft iron core. The resistor and the coil have the same resistance.

The switch is closed and lamp X lights instantly.

Which statement best describes lamp Y after the switch is closed?

A student investigated the behaviour of a spring under tension. The spring was hung vertically with a mass holder attached.

The position of the bottom of the mass holder was recorded. The spring was stretched by adding masses to the mass holder and the new positions were recorded. The extension of the spring each time was calculated.

The student produced the following table.

Criticise the student’s table.

The student used her data to plot a graph as shown.

Determine a value for the force constant k of the spring.

Two identical springs are joined in series and a bar magnet is hung from one end as shown.

The bar magnet is displaced a small distance vertically from its equilibrium position and released.

Calculate the frequency at which the system oscillates.

mass of magnet = 120 g spring constant of each spring = 22 N m⁻¹

*(d) Identical bar magnets are suspended from identical springs, with the North pole of each magnet inside a coil of wire as shown. The two coils are connected together with conducting leads.

Magnet A is displaced so that it oscillates vertically. The North pole of magnet A moves into and out of the coil of wire with simple harmonic motion. As this motion continues, magnet B starts to oscillate. The amplitude of oscillation of magnet B increases over time.

Explain why magnet B starts to oscillate with an increasing amplitude.