Question

A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The number of turns is n and the cross-sectional area of the coil is $A$. When the coil turns through $180^{\circ}$ about its diameter, the charge flowing through the coil is $Q$. The total resistance of the circuit is $R$. What is the magnitude of the magnetic induction?

• A. $\frac{QR}{nA}$
• B. $\frac{2QR}{nA}$
• C. $\frac{QR}{2RA}$
• D. $\frac{QR}{2nA}$

Answer 1

Answer: (D)

$\frac{QR}{2nA}$

Answer 2

Induced charge $Q=-\frac{n B A}{R}\left(\cos \theta_{2}-\cos \theta_{1}\right)$
$=-\frac{n B A}{R}\left(\cos 180^{\circ}-\cos 0^{\circ}\right)$
$\Rightarrow B=\frac{Q R}{2 n A}$