Question

A rectangular coil of 250 turns having length $2.1$ $cm$ and width $1.25$ $cm$ carries a current of $85$ $\mu A$. It is subjected to a magnetic field of strength $0.85$ $T$. Work done for rotating the coil by $180°$against the torque is approximately

• A. $4.44$ $\mu J$
• B. $2.3$ $\mu J$
• C. $1.15$ $\mu J$
• D. $9.4$ $\mu J$

Answer 1

The correct option is D $9.4$ $\mu J$

Work done in rotating a coil
$W=MB\left(\cos \right({\theta }_1)-\cos ({\theta }_2\left)\right)$
When it is rotated by angle ${180}^0$ , then
$W=2MB=2\left(NiA\right)BGiven,N=250,i=85\mu AA=1.25\times 2.1\times {10}^{-4}{m}^{2}A=2.625\times {10}^{-4}{m}^{2}B=0.85T$ ...(1)
Putting the value in (1), we get
$W=2\times 250\times 85\times {10}^{-6}\times 2.625\times {10}^{-4}\times 0.85W=9.4\mu J$