A conducting rod AB is bent in the form of a semicircle of radius R. It is kept in a region of uniform magnetic field B such that plane of semicircle is perpendicular to magnetic field. This rod is being moved with a constant speed v perpendicular to AB. Find the emf developed between the ends.

Explanation

To find the electromotive force (emf) developed between the ends of a conducting rod bent in the form of a semicircle and moving in a magnetic field, we can follow these steps:

### Step 1: Understand the Setup
We have a conducting rod AB that is bent into a semicircle with radius \( R \). The semicircle is placed in a uniform magnetic field \( B \) such that the plane of the semicircle is perpendicular to the magnetic field. The rod is moving with a constant speed \( v \) perpendicular to the diameter AB.

### Step 2: Identify the Relevant Formula
The formula for the emf (\( \mathcal{E} \)) induced in a conductor moving in a magnetic field is given by:
\[
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