The dimensions of $\left(\frac{B^{2}}{\mu_{0}}\right)$ will be. (where $\mu_{0}$ is the permeability of free space and $B$ is the magnetic field)

The energies required to set up in a cube of side $10 \,cm$ $(i)$ a uniform electric field of $10^7 \,Vm^{-1}$ and (ii) a uniform magnetic field of $0.25 \,Wbm^{-2}$ are respectively about $(\mu_0=4 \pi \times 10^{-7} \,Hm^{-1}, \varepsilon_0=8.9 \times 10^{-12} \,Fm^{-1})$

$A$ uniform beam of positively charged particles is moving with a constant velocity parallel to another beam of negatively charged particles moving with the same velocity in the opposite direction,separated by a distance $d$. The variation of the magnetic field $B$ along a perpendicular line drawn between the two beams is best represented by:

$A$ $100$ turn closely wound circular coil of radius $10\; cm$ carries a current of $3.2\; A$.
$(a)$ What is the field at the centre of the coil?
$(b)$ What is the magnetic moment of this coil?
The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. $A$ uniform magnetic field of $2\; T$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field.
$(c)$ What are the magnitudes of the torques on the coil in the initial and final position?
$(d)$ What is the angular speed acquired by the coil when it has rotated by $90^{\circ}$? The moment of inertia of the coil is $0.1\; kg\; m^{2}$.

$A$ current-carrying closed loop in the form of a right-angled isosceles triangle $ABC$ is placed in a uniform magnetic field acting along $AB.$ If the magnetic force on the arm $BC$ is $\vec F,$ the force on the arm $AC$ is

$A$ closed loop $PQRS$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments $PS, SR$ and $RQ$ are $F_1, F_2$ and $F_3$ respectively and are in the plane of the paper and along the directions shown,the force on the segment $QP$ is