(ii) A circular coil of $100$ turns and radius $\left$\frac{10}{\sqrt{\pi}}\right$ \text{ cm}$ carrying current of $5\cdot0 \text{ A}$ is suspended vertically in a uniform horizontal magnetic field of $2\cdot0 \text{ T}$. The field makes an angle $30^\circ$ with the normal to the coil. Calculate : (I) the magnetic dipole moment of the coil, and (II) the magnitude of the counter torque that must be applied to prevent the coil from turning. OR (b) (i) Derive an expression for the force $\vec{F}$ acting on a conductor of length $\text{L}$ and area of cross-section $\text{A}$ carrying current $\text{I}$ and placed in a magnetic field $\vec{B}$. (ii) A part of a wire carrying $2\cdot0 \text{ A}$ current and bent at $90^\circ$ at two points is placed in a region of uniform magnetic field $\vec{B} = -(0\cdot50 \text{ T}) \ \hat{k}$, as shown in the figure. Calculate the magnitude of the net force acting on the wire.