A-level Physics (Advancing Physics)/Induction

A magnetic field creates a current in a wire moving through it. This process is known as induction.

Flux Linkage
A magnetic field going through a coil of wire has a property known as flux linkage. This is the product of the flux &Phi; and the number of coils in the wire N.

Faraday's Law
Electric current is only induced in a coil of wire if the magnetic field is moving relative to the coil. Faraday's Law gives the electromotive force (emf) &epsilon; produced in a coil by a magnetic field:

$$\epsilon = -N\frac{d\Phi}{dt}$$

In other words, the emf (electric potential) induced in the coil is proportional to the rate of change of flux linkage. In practice, this means that if the coil is stationary relative to the magnetic field, no emf is induced. In order to induce emf, either the coil or the magnetic field must move. Alternatively, we may change the number of coils, for example, by crushing the coil, or pressing a switch which added more coils into the circuit, or moving more of the coils into the magnetic field.

Faraday's Law also works the other way. If we were to integrate both sides and rearrange the formula in terms of &Phi;, we would find that the flux depends on the integral of the voltage - not on its rate of change. If we put an emf across a coil, it induces a magnetic field. The flux does not depend on the rate of change of emf, but the emf does depend on the rate of change of the flux linkage.

Lenz's Law
Lenz's Law describes the direction of the current / emf induced by a change in magnetic flux. It states that current induced opposes the magnetic field. It does this by creating its own magnetic field. This explains the minus sign in Faraday's Law. This also means that the flux induced by a current (not a change in current) is proportional to the current, since the flux is produced in response to the current.

So, a change in flux induces a current and a voltage which is proportional to the rate of change of flux. This fits with Ohm's Law (V = IR). A current and a voltage in a coil induce a flux which is proportional to the current and the voltage.

Questions
1. What is the flux linkage of a 30 cm coil of 0.5mm thick wire with a flux perpendicular to it of 10Wb?

2. If the above coil is crushed steadily over a period of 2s, what emf is maintained?

3. The flux in a flux circuit varies according to the equation &Phi; = sin &omega;t. What is the equation for the emf induced?

4. Using a constant k, what is the equation for a current which could induce the flux in the flux circuit above?

5. Draw a graph of the flux, flux linkage, emf and current as deduced in the previous two questions.

/Worked Solutions/