(a) Derive the expression for the torque acting on a current carrying placed in a magnetic field.
(b) Explain the significance of a radial magnetic when current carrying coil is kept in it.

Explanation

### Solution:

**(a) Derivation of the Expression for Torque on a Current-Carrying Loop in a Magnetic Field:**

1. **Consider a rectangular coil**: Let’s assume we have a rectangular coil with sides AB and CD, and it is placed in a uniform magnetic field \( \mathbf{B} \). The current \( I \) flows through the coil.

2. **Identify forces on the coil**: The magnetic field exerts a force on the sides of the coil. The force on side AB (let's denote it as \( F_1 \)) and the force on side CD (denote it as \( F_2 \)) can be calculated using the formula for the magnetic force on a current-carrying conductor:
\[
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