State the Lorenz's force and express it in vector form. Which pair of vectors are always perpendicular to each other? Derive the expression for the force acting on a current carrying conductor of length L in a uniform magnetic field 'B'.

Explanation

### Step-by-Step Solution

**Step 1: State the Lorentz Force**
The Lorentz force is the force experienced by a charged particle moving in an electromagnetic field. It is given by the equation:
\[ \mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B}) \]
where:
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