Derive the expression for the torque acting on a current carrying loop placed in a magnetic field.

Derive the expression for the torque acting on the rectangular current carrying coil of a galvanometer. Why is the magnetic field made radial?

An $\alpha$-particle is accelerated through a potential difference of $10 \mathrm{kV}$ and moves along the x-axis. It enters in a region of the uniform magnetic field $\mathrm{B}=2\times {10}^{-3} \mathrm{T}$ acting the y-axis. Find the radius of its path. (Take mass of  $\alpha$-particle$=6.4\times {10}^{-27} \mathrm{kg}$)