A long wire carrying a steady current I lies in the plane of circular conducting loop placed at a certain distance from the wire. There will be an induced current in the loop if it is

Options

A. moved parallel to the wire
B. roatated about an axis perpendicular to the plane of the loop passing through the centre of the loop
C. rotated about an axis parallel to the wire passing through the centre of the loop
D. moved away from the wire

Answer

To determine when there will be an induced current in a circular conducting loop placed at a certain distance from a long wire carrying a steady current \( I \), we can analyze the situation based on the principles of electromagnetic induction.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a long wire carrying a steady current \( I \).
- A circular conducting loop is placed at a distance \( r \) from the wire.
- The magnetic field \( B \) created by the long wire at a distance \( r \) is given by Ampere's Law:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
- Here, \( \mu_0 \) is the permeability of free space.

2. **Induced Current Condition**:
- According to Faraday's Law of Electromagnetic Induction, an induced current will occur in the loop if there is a change in magnetic flux \( \Phi \) through the loop over time.
- The magnetic flux \( \Phi \) through the loop is given by:
\[ \Phi = B \cdot A \]
- Where \( A \) is the area of the loop.

3. **Analyzing Different Scenarios**:
- **Option 1: Move Parallel to the Wire**:
- If the loop is moved parallel to the wire, the distance \( r \) remains constant.
- Since \( B \) is constant, the magnetic flux \( \Phi \) remains constant.
- Therefore, there is no change in flux, and the induced current is zero.

- **Option 2: Rotate about an Axis Perpendicular to the Plane of the Loop**:
- Rotating the loop about an axis perpendicular to its plane does not change the area \( A \) or the magnetic field \( B \).
- Thus, the magnetic flux \( \Phi \) remains constant, leading to zero induced current.

- **Option 3: Rotate about an Axis Parallel to the Wire**:
- If the loop is rotated about an axis parallel to the wire, the area \( A \) of the loop changes.
- This change in area leads to a change in magnetic flux \( \Phi \).
- Therefore, an induced current will be generated in this scenario.

- **Option 4: Move Away from the Wire**:
- As the loop moves away from the wire, the distance \( r \) increases.
- This results in a decrease in the magnetic field \( B \) (since \( B \) is inversely proportional to \( r \)).
- Consequently, the magnetic flux \( \Phi \) changes, leading to an induced current.

4. **Conclusion**:
- Induced current occurs in the following scenarios:
- When the loop is rotated about an axis parallel to the wire (Option 3).
- When the loop is moved away from the wire (Option 4).
- Therefore, Options 3 and 4 are correct.