Question

A galvanometer coil has 500 turns and each turn has an average area of \(3\times10^{-4}\ \mathrm{m^2}\). If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.

Hint:

The torque on a current coil is \(\tau = NIAB\sin\alpha\), where \(\alpha\) is the angle between B and the coil's area vector; for a coil whose plane is parallel to the field, \(\alpha = 90^\circ\) and the torque is maximum.

Answer 1

Correct Answer: 20

Torque on a coil: \(\tau = NIAB\sin\alpha\). With the plane of the coil parallel to B, \(\alpha = 90^\circ\) and \(\tau = NIAB\).
\(B = \dfrac{\tau}{NIA} = \dfrac{1.5}{500\times0.5\times3\times10^{-4}} = \dfrac{1.5}{7.5\times10^{-2}} = 20\) T.
Answer: 20