A charge q of mass m is moving with a velocity of V, at right angles to a uniform magnetic field B. Deduce the expression for the radius of the circular path it describes.

Explanation

To derive the expression for the radius of the circular path described by a charge \( q \) of mass \( m \) moving with a velocity \( V \) at right angles to a uniform magnetic field \( B \), we can follow these steps:

### Step 1: Understand the Forces Acting on the Charge
When a charged particle moves in a magnetic field, it experiences a magnetic force given by the Lorentz force law:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]
Since the velocity \( \mathbf{v} \) is perpendicular to the magnetic field \( \mathbf{B} \), the angle between them is \( 90^\circ \). Thus, we can simplify the expression for the magnetic force:
...