Question

A moving-coil galvanometer has a 50-turn coil of size 2 cm × 2 cm. It is suspended between the magnetic poles producing a magnetic field of 0.5 T. Find the torque on the coil due to the magnetic field when a current of 20 mA passes through it.

Answer 1

Given:
Number of turns in the coil, n = 50
Area of the cross section of the coil, A = 2 cm × 2 cm = 2 × 2 × 10⁻⁴ m²
Current flowing through the coil, I = 20 × 10⁻³ A
Magnetic field strength due to the presence of the poles, B = 0.5 T
The torque experienced by the coil placed in an external magnetic field $\left(\tau \right)$ is given by
$$\begin{gathered} \tau \mathit{=}nI\left(\overrightarrow{A}\mathit{\times }\overrightarrow{B}\right) \\ \Rightarrow \tau \mathit{=}nIAB\sin 90° \\ \Rightarrow \tau =50\times 20\times {10}^{-3}\times 4\times {10}^{-4}\times 0.5 \\ \Rightarrow \tau =2\times {10}^{-4}\mathrm{N}-\mathrm{m} \end{gathered}$$