Question

The effective radius of a circular coil is $R$ and the number of turns $N$. The current through it is $i$ ampere. The work done is rotation the coil from angle $\theta =0^o$ to $\theta ={180}^o$ in an external magnetic field $B$ will be.

• A. $\pi Ni{R}^{2}B$
• B. $2\pi Ni{R}^{2}B$
• C. $\left(\frac{2NiB}{\pi R^2}\right)$
• D. $4\pi Ni{R}^{2}B$

Answer 1

The correct option is B $2\pi Ni{R}^{2}B$

Work Done= $△$ change in P.E

$=nIA[\cos {\theta }_2-\cos \theta 1]B$

$=nIA[\cos 0-\cos 180]B$

$=Ni\pi R^2\left(2\right)B$

$=2\pi NI{R}^{2}B$