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: Understanding the Motion of the Rod
The rod is rotating about one end with an angular speed \( \omega \). As it rotates, different points along the length of the rod move with different linear velocities. The linear velocity \( v \) of a point at a distance \( r \) from the axis of rotation is given by:
\[ v = r \omega \]
where \( r \) varies from \( 0 \) to \( l \) (the length of the rod).
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