Question

A long solenoid of cross-sectional area 28𝑐𝑚2

A coil 𝐶 of 160 turns of insulated wire is wound tightly around the centre of the solenoid. If 𝑛 is a 

constant equal to 1.5 × 10

3𝑚−1

and 𝜇𝑜 is the permeability of free space, calculate for a current of 

3.5𝐴 in the solenoid; (i) the magnetic flux at the centre of the solenoid. (ii) the flux linkage in the 

coil 𝐶. (iii) If the current in the coil 𝐶 is reversed in 0.80𝑠, calculate the average e.m.f. induced in 

the coil 𝐶.

Answer 1

(i) The magnetic flux at the centre of the solenoid:

$$B=\mu_0nI=4\pi·10^{-7}·1.5·10^3·3.5=6.6·10^{-3}\text{ T}.$$

(ii) The flux linkage in the coil 𝐶:

$$\Phi=BAN=6.6·10^{-3}·25·10^{-4}·160=\\=3·10^{-3}\text{ Wb}.$$

(iii) If the current in the coil 𝐶 is reversed in 0.80𝑠, calculate the average e.m.f. induced in the coil 𝐶:

$$\text{e.m.f.}=\frac{\Delta \Phi}{\Delta t}=\frac{2\Phi}{\Delta t}=7.5·10^{-3}\text{ V}.$$