Question

A current carrying coil placed in a magnetic field $B$ experiences a torque $\tau$. If $\theta$ is the angle between the normal to the plane of the coil and field $B$ and $\varphi$ is the flux linked with the coil, then

• A. $\tau$ is minimum for $\theta=90^{\circ}$
• B. $\tau$ and $\varphi$ are maximum for $\theta=0^{\circ}$
• C. $\varphi$ is maximum for $\theta=90^{\circ}$
• D. $\tau$ and $\varphi$ are zero for $\theta=90^{\circ}$
• E. $\tau$ is zero and $\varphi$ is maximum for $\theta=0^{\circ}$

Answer 1

Answer: (E)

When a current carrying coil is placed in magnetic field $B$ experiences a torque which is given as
$\tau =M \times B$
$ =M B \sin \theta$
where, $M$ is the magnetic moment.
So, $\tau$ is maximum at $\theta=90^{\circ}$,
i.e. $\tau_{\max }=M B$
$\tau$ is minimum at $\theta=0$
i.e. $\tau_{\min }=0$
Now, the flux associated with the coil will be $\varphi=B \cdot A=B A \cos \theta$
So, $\varphi$ is maximum at $\theta=0$
$\Rightarrow \varphi_{\max }=B A$
$\varphi$ is minimum at $\theta=90^{\circ}$
$\Rightarrow \varphi_{\min }=0$