Two coils are placed close together in a physics lab to demonstrate Faraday’s law of induction. A current of in one is switched off in , inducing an emf in the other. What is their mutual inductance?

There are two rules in Faraday's Laws of Electromagnetic Induction. The first rule explains emf induction in a conductor, whereas the second law quantifies the emf generated.

The change in the current is,$∆I=5.00A$

Time in which current is switched off, $∆t=1.00ms\left(\frac{{10}^{-3}s}{1ms}\right)=1.00\times {10}^{-3}s$

The EMF induced in the other coil is,$\epsilon =9.00V$

The induced electromotive force can be expressed as,

$\epsilon =-\left(M\frac{∆I}{∆t}\right)$………….(1)

Where M is the mutual inductance, $∆I$is the change in the current in the time interval $∆t$.

Therefore, by rearranging equation (1), we can get mutual inductance such that,

$M=-\left(\frac{\epsilon ∆t}{∆I}\right)$

Substituting the given data in the above expression will result in,

$$\begin{gathered} M=-\left(\frac{\left(9.00V\right)\times \left(1.00\times {10}^{-3}s\right)}{5.00A}\right) \\ =-1.8\times {10}^{-3}H\left(\frac{1mH}{{10}^{-3}H}\right) \\ =-1.8mH \end{gathered}$$

Therefore, the value for mutual inductance is obtained as 1.8mH and the negative sign is due to the Lenz's law