Question

A rectangular coil of $100$ turns has length $5$ cm and width $4$ cm. It is placed with its plane parallel to a uniform magnetic field and a current of $2A$ is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is $0.2N{m}^{-1}$

Answer 1

$\tau =ni\overrightarrow{A}\times \overrightarrow{B}$

$\Rightarrow \tau =niAB\sin {90}^0\Rightarrow 0.2=100\times 2\times 5\times 4\times {10}^{-4}\times B$

$\Rightarrow B=\frac{0.2}{100\times 2\times 5\times 4\times {10}^{-4}}=0.5Tesla$