A-level Physics (Advancing Physics)/Induction/Worked Solutions

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

$$N = \frac{30 \times 10^{-2}}{0.5 \times 10^{-3}} = 600\mbox{ coils}$$

$$N\Phi = 600 \times 10 = 6000\mbox{ Wb}$$

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

$$\mid \epsilon \mid = \frac{dN\Phi}{dt} = \frac{6000}{2} = 3000\mbox{ V}$$

This principle of removing the flux linkage rapidly (although not usually by destroying one's equipment) is used to create very high voltages for short periods of time.

'''3. The flux in a flux circuit varies according to the equation &Phi; = sin &omega;t. What is the equation for the emf induced?'''

$$\epsilon = -\frac{dN\Phi}{dt} = -N\frac{d}{dt}\sin{\omega t} = -N\omega\cos{\omega t}$$

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

$$I = -k\sin{\omega t}$$

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

In order to keep the scales sane, I used a 2-coil (N=2) coil to plot the following graph:



Remember that the current here is inducing the flux (and flux linkage), which is in turn inducing the emf.