A conducting rod of length l is moving in a transverse magnetic field of strength B with veocity v. The resistance of the rod is R. The current in the rod is

Options

A. `(Blv)/(R)`
B. Blv
C. zero
D. `(B^(2)v^(2)l^(2))/(R)`

Answer

To find the current in a conducting rod of length \( l \) moving in a transverse magnetic field of strength \( B \) with velocity \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a conducting rod of length \( l \) moving with a velocity \( v \) in a magnetic field \( B \).
- The motion of the rod is perpendicular (transverse) to the direction of the magnetic field.

2. **Induced EMF Calculation**:
- According to Faraday's law of electromagnetic induction, when a conductor moves through a magnetic field, an electromotive force (EMF) is induced across the ends of the conductor.
- The formula for the induced EMF (\( \mathcal{E} \)) in a rod moving in a magnetic field is given by:
\[ \mathcal{E} = B \cdot l \cdot v \]
- Here, \( B \) is the magnetic field strength, \( l \) is the length of the rod, and \( v \) is the velocity of the rod.

3. **Current Calculation**:
- The current (\( I \)) induced in the rod can be calculated using Ohm's law, which states that current is equal to the induced EMF divided by the resistance (\( R \)) of the rod.
- Therefore, the current can be expressed as:
\[ I = \frac{\mathcal{E}}{R} = \frac{B \cdot l \cdot v}{R} \]

4. **Final Expression**:
- Thus, the current in the rod is given by:
\[ I = \frac{B \cdot l \cdot v}{R} \]

### Final Answer:
The current in the rod is \( I = \frac{B \cdot l \cdot v}{R} \).

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