(a) A circular coil of 30 turns and radius $8.0\text{ cm}$ carrying a current of $6\text{ A}$ is suspended vertically in a uniform horizontal magnetic field of $1.0\text{ T}$. The field lines make an angle of $30^{\circ}$ with the plane of the coil. Calculate the magnitude of the external torque that must be applied to prevent the coil from turning. What would happen if the circular coil is replaced by a planar coil of irregular shape that encloses the same area, keeping other parameters unchanged? OR (b) An alpha particle (mass $6.4 \times 10^{-27}\text{ kg}$ and charge $3.2 \times 10^{-19}\text{ C}$) having $8.0\text{ MeV}$ energy, enters a region of a uniform magnetic field of $0.5\text{ T}$. If the field is directed perpendicular to the velocity of the particle, find the radius of the circular path described by the particle. Mention the condition under which the particle in this region (i) describes a helical path, and (ii) goes straight undeviated.