2024 A/L Physics Past Paper · Question 11 (English Medium)

Answer: (2) law of conservation of energy.

What the question asks

This question is about producing electricity by changing a magnetic flux.

Imagine pushing a magnet towards a coil of wire. An electromotive force is induced. If the circuit is closed, a current can flow.

What we must find: which conservation law is connected with this induction.

How we find it: look at why the induced effect opposes the change. Then ask where the electrical energy comes from.

No numerical quantities are given. Follow the changing magnetic flux, the induced opposition and the transfer of energy.

$E$ ($\text{V}$): induced electromotive force.

$W$ ($\text{J}$): external work.

$U_e$ ($\text{J}$): electrical energy.

$U$ ($\text{J}$): total energy of the closed system. It includes the person pushing, the coil, the lamp and its surroundings.

Relevant theory

The magnitude of the electromotive force induced in a conducting coil or a circuit at any instant is directly proportional to the rate of change of the magnetic flux or the flux linkage number intersecting it at that instant.

The direction of the induced electromotive force is such that its current flows in a direction opposing the change of flux causing it.

The total energy of a closed system remains constant. However, within a system one form of energy can get converted into another form of energy.

What is happening: a south pole approaching the coil increases its magnetic flux. With a closed circuit, the induced current makes the near end of the coil a south pole too. The coil therefore opposes the approach.

To keep pushing the magnet forwards, an external agent must do work. That work supplies the electrical energy. Induction does not create energy from nothing.

For example, push a magnet towards a closed wire coil connected to a small lamp. While the flux changes, an induced current can light the lamp.

Your push has to overcome the induced opposition. The energy you supply appears as electrical energy and then as light and heat.

In words: doing work provides the energy delivered by induction.

Reading the options

The connection is conservation of energy, option (2). Faraday’s law gives the induced electromotive force. Lenz’s law gives its opposing direction. So the energy must be supplied from outside. Induction does not create it.

Charge conservation, an interaction-force pair, angular momentum conservation and linear momentum conservation do not identify this energy balance.

Independent check: imagine the induced effect helped the change on both approach and withdrawal. Complete a cycle, returning the magnet and apparatus to their initial states. Electrical energy and extra mechanical work would then have appeared without equivalent energy input. This would violate conservation of energy. The opposing direction avoids this contradiction.

Why the other options fail

This confuses the flow of charge with the source of electrical energy. Charge conservation does not explain why the induced effect opposes the change of magnetic flux. The work needed against that opposition supplies the energy.

Equal and opposite interaction forces do not by themselves identify the energy source. The relevant link here is that doing work against the induced opposition provides electrical energy.

This selects a rotational conservation law because generators can rotate. But a translating magnet also induces an electromotive force in a coil. The common link is the conversion of supplied work into electrical energy.

This follows the magnet’s motion rather than the energy transfer. Maintaining its motion against the induced opposition requires external work. It is conservation of energy that connects that work to the electrical output.

Conclusion

The related law is conservation of energy. The answer is (2).