Prove that the force acting on a current carrying wire, joining two fixed points a and b in a uniform magnetic field, is independent of the shape of the wire.

Explanation

To prove that the force acting on a current-carrying wire, joining two fixed points A and B in a uniform magnetic field, is independent of the shape of the wire, we can follow these steps:

### Step 1: Understand the Force on a Current-Carrying Wire
The force \( \mathbf{F} \) acting on a current-carrying wire in a magnetic field is given by the formula:
\[ \mathbf{F} = I \mathbf{L} \times \mathbf{B} \]
where:
...