A rod of length l is translating at a velocity v making an angle `theta` with its length. A uniform magnetic field B exists in a direction perpendicular to the plane of motion. Calculate the emf induced In the rod, Draw a figure representing the induced emf by on equivalent battery.

Explanation

The situation is shown in figure
The component of the velocity perpendicular to the length of the rod is `v_|_ = sin theta`
Only this component is effective in producing the emf in the rod
As the magnetic field is perpendicular to the plane of motion, the emf induced across the ends is ` epsilon = v _|_ Bl = vBl sin theta`
In the figure shown, the positive charges of the rod shift towards left due to the force `vec qu X vecB
Thus, the left side of the rod is electrically positive
Figure shows the equivalent battery