A metallic rod of length l is rotated at a constant angular speed `omega`, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.

Explanation

To derive the expression for the current induced in a metallic rod of length \( l \) rotating at a constant angular speed \( \omega \) in a uniform magnetic field \( B \), we can follow these steps:

### Step 1: Understand the Setup
Consider a metallic rod of length \( l \) that is rotating about one of its ends in a plane perpendicular to a uniform magnetic field \( B \). The rod sweeps out an area as it rotates.

### Step 2: Determine the Area Swept by the Rod
The area \( A \) swept by the rod after rotating through an angle \( \theta \) is given by:
\[
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