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 ${180}^o$ 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. $\frac{Qn}{2RA}$
• D. $\frac{QR}{2nA}$

Answer 1

The correct option is D $\frac{QR}{2nA}$

emf induced $e=n\omega AB$

induced charge $Q=\frac{-nBA}{R}(\cos {\theta }_2-\cos {\theta }_1)$

$=\frac{-nBA}{R}(\cos 180°-\cos 0°)$

$=\frac{2nBA}{R}$

$B=\frac{QR}{2nA}$

where ,$A$=area of cross section of coil.

$n$=number of turns.