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 $\phi$ is the flux linked with the coil, then

• A. $\tau$ is minimum for $\theta =90^{\circ }$
• B. $\tau$ and $\phi$ are maximum for $\theta =0^{\circ }$
• C. $\phi$ is maximum for $\theta =90^{\circ }$
• D. $\tau$ and $\phi$ are zero for $\theta =90^{\circ }$
• E. $\tau$ is zero and $\phi$ 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
$\tau =M\times B$
$=MB\sin \theta$
where, $M$ is the magnetic moment.
So, $\tau$ is maximum at $\theta =90^{\circ }$,
i.e. ${\tau }_{\max }=MB$
$\tau$ is minimum at $\theta =0$
i.e. ${\tau }_{\min }=0$
Now, the flux associated with the coil will be $\phi =B\cdot A=BA\cos \theta$
So, $\phi$ is maximum at $\theta =0$
$\Rightarrow {\phi }_{\max }=BA$
$\phi$ is minimum at $\theta =90^{\circ }$
$\Rightarrow {\phi }_{\min }=0$