(a) State the laws of electromagnetic induction (b) Explain how one of the laws illustrates the principle of conservation of energy (c)(i) Draw a labelled d...

(a) Laws of electromagnetic induction

Faraday's law: Whenever there is a change in the magnetic flux linking a circuit, an e.m.f. is induced in the circuit, and the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage, \(E \propto -\dfrac{d\Phi}{dt}\).

Lenz's law: The induced current (or e.m.f.) always flows in such a direction as to oppose the change producing it.

(b) How Lenz's law illustrates conservation of energy

Lenz's law states that the induced current opposes the change that causes it. Therefore, to keep the flux changing (for example, to keep pushing a bar magnet into a coil) an external agent must do work against the opposing force set up by the induced current. The mechanical (kinetic) energy supplied by the external agent is exactly converted into the electrical energy of the induced current (which finally appears as heat in the resistance of the circuit). If the induced current instead aided the motion, the system would accelerate itself and create energy from nothing. Hence Lenz's law is simply a statement of the principle of conservation of energy.

(c)(i) Simple d.c. electric motor

It consists of a rectangular coil of insulated wire (the armature) mounted on an axle between the poles of a permanent magnet, a split-ring commutator fixed to the coil, and two carbon brushes that press against the commutator and feed current from a d.c. supply (battery).

Action: When current flows through the coil, side AB and side CD each lie in the magnetic field and carry current, so by the motor rule (Fleming's left-hand rule) each side experiences a force. On side AB the force acts upward and on side CD it acts downward (the two forces are equal and opposite), producing a couple (turning moment) that rotates the coil. As the coil passes the vertical position the split-ring commutator reverses the direction of current in the coil, so the forces on the two sides continue to turn the coil in the same direction, giving continuous rotation.

(c)(ii) Two reasons why efficiency is less than 100%

1. Some energy is wasted as heat in the coil windings because of their electrical resistance (\(I^{2}R\) heating).
2. Energy is lost through friction at the bearings and between the brushes and commutator (and through air resistance), so the useful mechanical output is always less than the electrical input.