Electromagnetic induction

This question is about comparing two methods for storing energy.

A proposed method for storing energy uses trucks powered by electric motors.

The trucks carry sand up a mountain, storing surplus energy as gravitational potential energy.

When the energy needs to be released, they carry the sand back down the mountain, converting the gravitational potential energy into chemical energy stored in a battery.

Explain how an electrical generator in the truck could use electromagnetic induction to convert gravitational potential energy into chemical energy stored in a battery.

A second proposed method for storing energy uses a tank of wax.

The wax is heated using an electrical heater, storing surplus energy as internal energy of the wax. The wax increases in temperature and melts as it is heated.

When the energy needs to be released, the wax is allowed to cool, converting the internal energy of the wax into thermal energy.

Explain, in terms of the particles in the wax, how energy is stored when it is heated.

18* (a) Describe how an experiment can be conducted to determine how the output current of a step‑up transformer depends on the number of turns on the secondary coil.

Explain how the data collected can be analysed to establish the relationship between the output current and the number of turns on the secondary coil.

You are provided with wire and a suitable core on which to wind the wire, as well as any other normal laboratory equipment.

Use the space below to draw a labelled circuit diagram.

State Faraday’s law.

Show that the number of turns on the secondary coil is 20.

At one particular instant, the output voltage from the transformer is 3.4 V.

Calculate the change in magnetic flux experienced by the secondary coil in a short time interval of 1.2 ms and state its unit.

Assume that the output voltage from the transformer remains constant at 3.4 V over this time interval.

The length of an unloaded spring is approximately 4 cm.

The force constant k of the spring is 0.62 N cm^–1.

Describe how you could determine k using an appropriate experiment.

Calculate the magnitude of the block’s initial acceleration at the instant that the force F is removed.

Assume that the spring is not extended beyond its limit of proportionality.

acceleration =........ m s^–2

The block now moves with simple harmonic motion.

Calculate the frequency of this motion.

The block is replaced by a strong magnet L of slightly greater mass.

The oscillation frequency of this new arrangement is 2.5 Hz.

The magnet L is placed inside a coil X of insulated copper wire.

The coil X is connected with long wires to a second, identical coil Y.

A second strong magnet M is placed inside Y and attached to a vibration generator.

The vibration generator is then forced to oscillate with a frequency of approximately 2.5 Hz by

As magnet M oscillates, it moves in and out of coil Y.

........

The frequency of the vibration generator is now varied between 0.5 Hz and 5.0 Hz.

Suggest how the amplitude and frequency of the oscillations of L will change as the frequency of the generator is varied.

You may draw a diagram to support your answer.

The diagram below shows two insulated-copper coils A and B connected in circuits.

Both coils are individually wrapped around the same iron rod. Coil A is connected to a cell and a switch. Coil B is connected to a filament lamp.

The switch is initially closed and the lamp is off.

The switch is then opened. The lamp flashes on for a brief time, and then remains off.

Explain these observations in terms of magnetic flux.

A student is carrying out an experiment using a search coil.

A long solenoid is connected to an alternating current supply.

The search coil is placed at one end of the solenoid. The plane of the search coil is tilted such that it makes an angle with the central axis of the solenoid. The maximum alternating induced electromotive force (e.m.f.) across the ends of the search coil is E₀.

Name an instrument that can be used to determine E₀.

The equation for E₀ is:

E₀ = K I₀ANf sin

where I₀ = maximum current in the solenoid, A = cross-sectional area of the search coil, N = number of turns of the search coil, f = frequency of the alternating current in the solenoid and K = 4.0 × 10^–3 V A^–1 m^–2 s.

The magnitude of the induced e.m.f. in the search coil can be determined using Faraday’s law of electromagnetic induction:

e.m.f. = rate of change of magnetic flux linkage

In the experiment, angle is changed and E₀ measured.

Suggest the quantity, or quantities, in the equation E₀ = K I₀ANf sin linked to

1 the ‘rate’ part of the law

2 the ‘change of magnetic flux linkage’ part of the law.

The student plots a straight-line graph of E₀ against sin .

Determine f, including the absolute uncertainty. Write your value of f to 2 significant figures.

I₀ = (8.0 ± 0.2) A

f =........ ±........ Hz

Faraday’s law of electromagnetic induction is written below with two terms missing.

The........ induced in a circuit is directly proportional to the rate of change of

magnetic flux........

What are the two missing terms?

A current, density

B current, linkage

C electromotive force, density

D electromotive force, linkage

Your answer

The diagram below shows two long vertical current-carrying wires X and Y.

The direction of the current in each wire is the same.

Explain why wire Y experiences a force and deduce the direction of this force.

State Faraday’s law of electromagnetic induction.

Explain the shape of the curve in Fig. 3.3.

The torch is inverted 80 times.

Calculate the total energy stored in the capacitor.

Fig. 21.1 shows a coil of a simple generator rotating in a uniform magnetic field.

The coil has 85 turns of insulated wire. The cross-sectional area of the coil is 14 cm². Fig. 21.2 shows the variation of magnetic flux density B through the plane of the coil with time it rotates.

Explain why the electromotive force (e.m.f.) induced across the ends of the coil is a maximum at the times when B = 0.

Draw a tangent to the curve in Fig. 21.2 when B = 0, and hence determine the maximum e.m.f. induced across the ends of the coil.

maximum e.m.f. =........ V

Fig. 21.3 shows the variation of the e.m.f. induced across the ends of the coil with time t.

The magnitude of the magnetic flux density of the uniform field is now halved and the coil is rotated at twice its previous frequency.

On Fig. 21.3 sketch the new variation of the e.m.f. induced with time t.

Explain the shape of the graph in terms of the magnetic flux linking the coil.

The coil shown in Fig. 5.1 has 150 turns. The maximum induced e.m.f. V₀ across the coil is 1.2 V when the magnet is rotating at 24 revolutions per second.

Calculate the maximum magnetic flux through the coil using the equation

V₀ = 2π × (frequency) × (maximum magnetic flux linkage)

Give a unit with your answer.

* A student is given a transformer with coils X and Y, as shown in Fig. 5.4.

The student is intending to investigate how the maximum induced e.m.f. V₀ in coil Y depends on the frequency f of the alternating current in coil X.

The changing magnetic flux density in coil X induces an e.m.f. in coil Y. Faraday’s law indicates that the maximum induced e.m.f. V₀ should be directly proportional to f.

Describe how you would investigate the suggested relationship between V₀ and f in the laboratory using these coils. In your description include all of the equipment used and how you would analyse the data collected.

Use the space below to draw a suitable diagram.

* A student conducts an experiment to confirm that the uniform magnetic flux density B between the poles of a magnet is 30 mT.

A current-carrying wire of length 5.0 cm is placed perpendicular to the magnetic field.

The current I in the wire is changed and the force F experienced by the wire is measured. Fig. 22.1 shows the graph plotted by the student.

The student’s analysis is shown on the graph of Fig. 22.1 and in the space below.

F = BIL

This is just 2 mT out from the 30 mT value given by the manufacturer, so the experiment is very accurate.

Evaluate the information from Fig. 22.1 and the analysis of the data from the experiment. No further calculations are necessary.

Use Faraday’s law of electromagnetic induction to explain why the filament lamp is lit.

The primary coil has 400 turns and the secondary coil has 20 turns. The potential difference across the lamp is 12 V and it dissipates 24 W. The transformer is 100% efficient.

1. Calculate the current in the primary coil.

2. The alternating voltage supply is replaced by a battery and an open switch in series. The switch is closed. The lamp is lit for a short period of time and then remains off. Explain this observation.