Question

A current-carrying circular coil of magnetic moment $M$ is situated in a magnetic field $B$. The work done in deflecting it from an angle $0^o$ to ${\theta }^o$ will be :

• A. $MB$
• B. $MB(1-cos\theta )$
• C. $-MB$
• D. $MB(1-sin\theta )$

Answer 1

The correct option is B $MB(1-cos\theta )$

Work done = dw = Fd$\theta$ = $MB\sin \theta d\theta$

$\int dw$ = ${\int }_{{\theta }_2}^{{\theta }_1}MB\sin \theta d\theta$

$\Rightarrow W=MB{\int }_{{\theta }_2}^{{\theta }_1}\sin \theta d\theta =MB{[-\cos \theta ]}_{{\theta }_1}^{{\theta }_2}$

$\Rightarrow W=MB[\cos {\theta }_1-\cos {\theta }_2]$

$\therefore {\theta }_1=\theta and{\theta }_2=\theta$

$\Rightarrow W=MB[\cos \theta -\cos \theta ]$

$\Rightarrow W=MB[1-\cos \theta ]$