A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statements(s) from the following

Options

A. The entire rod is at the same electric potential.
B. There is an electric field in the rod.
C. The electric potential is highest at the centre of the rod and decreases towards its ends.
D. The electric potential is lowest at the centre of the rod, and increases towards its ends.

Explanation

To analyze the situation described in the question, we need to apply the principles of electromagnetic induction, specifically Faraday's law and the Lorentz force.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a metal rod (let's call it rod AB) that is moving with a constant velocity \( v \) in a direction perpendicular to its length.
- There is a uniform magnetic field \( B \) that is also perpendicular to both the rod and its direction of motion.

2. **Applying the Lorentz Force**:
- As the rod moves through the magnetic field, the charges (electrons) within the rod experience a force due to the magnetic field. This force is given by the Lorentz force equation:
\[ F = q(\vec{v} \times \vec{B}) \]
- Here, \( q \) is the charge of the electrons, \( \vec{v} \) is the velocity of the rod, and \( \vec{B} \) is the magnetic field.

3. **Direction of the Force**:
- The direction of the force can be determined using the right-hand rule. If you point your thumb in the direction of the velocity of the rod and your fingers in the direction of the magnetic field, your palm will face the direction of the force acting on positive charges (which is opposite to the direction of the force acting on negative charges like electrons).
- This results in a separation of charges within the rod, creating an electric field.

4. **Induced Electromotive Force (EMF)**:
- The separation of charges leads to a potential difference (voltage) across the ends of the rod. This induced voltage (or EMF) can be calculated using the formula:
\[ \text{EMF} = B \cdot L \cdot v \]
- Where \( L \) is the length of the rod.

5. **Conclusion**:
- The moving rod in a magnetic field induces an electromotive force due to the motion of the charges within it. The rod will have a higher potential at one end and a lower potential at the other end, leading to a potential difference across the rod.