Question

Figure shows an insulating sphere of mass M and radius R with N turns of wire wrapped around it. Plane of coil is parallel to incline. A uniform magnetic field along vertical exist in space. If $\theta ={45}^{\circ }$ and $\mu =0.5$ and current in wire is 'i',then

• A. Minimum current required to keep sphere in rotational equilibrium is $\frac{Mg}{2NBR\pi }$
• B. Minimum current required to keep sphere in rotational equilibrium is $\frac{Mg}{N\pi RB}$
• C. Sphere cannot be in translational equilibrium
• D. Sphere can remain at rest

Answer 1

Answer: (A), (C)

The correct options are
A Minimum current required to keep sphere in rotational equilibrium is $\frac{Mg}{2NBR\pi }$
C Sphere cannot be in translational equilibrium


For rotational equilibrium ${\tau }_{net}=0$
i.e. $f_{l}R={\mu }_{0}Bsin\theta$
As $f_l=\mu Mgcos\theta$
So $f_l<Mgsin\theta$
So no translational equilibrium and $f_l=\mu Mgcos\theta$
$\mu Mgcos\theta R={\mu }_{0}Bsin\theta$
$\mu Mgcos\theta R=Ni\pi R^{2}Bsin\theta \Rightarrow i=\frac{\mu Mg}{N\pi RBtan\theta }$
$i=\frac{Mg}{2\pi NBR}$