Deduce the expression for the frequency of revolution of a charged particle in a magnetic field and show that this is independent of the velocity or energy of the particle.

Explanation

To deduce the expression for the frequency of revolution of a charged particle in a magnetic field, we will follow these steps:

### Step 1: Understand the Magnetic Force on a Charged Particle
When a charged particle with charge \( Q \) moves with velocity \( \mathbf{V} \) in a magnetic field \( \mathbf{B} \), it experiences a magnetic force given by:
\[ \mathbf{F} = Q (\mathbf{V} \times \mathbf{B}) \]
The magnitude of this force can be expressed as:
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