An infinitely long cylinder is kept parallel to an uniform magnetic field B directed along positive z-axis. The direction of induced current as seen from the z-axis will be

Options

A. clockwise of the positive Z-axis
B. anti positive Z-axis clockwise of the positive z-axis
C. zero
D. along the magnetic field

Explanation

To determine the direction of the induced current in an infinitely long cylinder kept parallel to a uniform magnetic field directed along the positive z-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have an infinitely long cylinder placed parallel to a uniform magnetic field \( \mathbf{B} \) that is directed along the positive z-axis.

2. **Magnetic Flux Calculation**:
- The magnetic flux \( \Phi \) through the cylinder is given by the formula:
\[ \Phi = \mathbf{B} \cdot \mathbf{A} = B A \cos \theta \]
- Here, \( \theta \) is the angle between the magnetic field \( \mathbf{B} \) and the area vector \( \mathbf{A} \) of the surface of the cylinder. Since the cylinder is parallel to the magnetic field, \( \theta = 90^\circ \).

3. **Evaluating the Flux**:
- Since \( \cos 90^\circ = 0 \), the magnetic flux through the cylinder becomes:
\[ \Phi = B A \cdot 0 = 0 \]
- This indicates that there is no magnetic flux through the cylinder.

4. **Induced EMF and Current**:
- According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) \( \mathcal{E} \) is given by:
\[ \mathcal{E} = -\frac{d\Phi}{dt} \]
- Since \( \Phi = 0 \), it follows that:
\[ \frac{d\Phi}{dt} = 0 \implies \mathcal{E} = 0 \]
- If the induced emf is zero, then the induced current \( I \) in the circuit is also zero, as given by Ohm's law:
\[ I = \frac{\mathcal{E}}{R} = \frac{0}{R} = 0 \]

5. **Conclusion**:
- Since there is no induced current in the cylinder due to the absence of changing magnetic flux, the direction of the induced current as seen from the z-axis is **none**. Therefore, the correct answer is that there is no induced current.