A conducting circular loop of radius r carries a constant current i. It is placed in a uniform magnetic field B such that B is parallel to the plane of the loop. The magnetic torque acting on the loop is-

Options

A. irB
B. `2pi r iB`
C. zero
D. `pir^(2)iB`

Explanation

To solve the problem of finding the magnetic torque acting on a conducting circular loop in a uniform magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- A conducting circular loop of radius \( r \) carries a constant current \( i \).
- The loop is placed in a uniform magnetic field \( B \) that is parallel to the plane of the loop.

2. **Understand the Concept of Torque**:
- The magnetic torque \( \tau \) acting on a current-carrying loop in a magnetic field is given by the formula:
\[ \tau = \mathbf{m} \times \mathbf{B} \]
- Where \( \mathbf{m} \) is the magnetic moment of the loop.

3. **Calculate the Magnetic Moment**:
- The magnetic moment \( \mathbf{m} \) for a loop is given by:
\[ \mathbf{m} = i \cdot A \]
- Here, \( A \) is the area of the loop. For a circular loop, the area \( A \) is:
\[ A = \pi r^2 \]
- Therefore, the magnetic moment can be expressed as:
\[ \mathbf{m} = i \cdot \pi r^2 \]

4. **Determine the Angle Between \( \mathbf{m} \) and \( \mathbf{B} \)**:
- Since the magnetic field \( B \) is parallel to the plane of the loop, the angle \( \theta \) between the magnetic moment \( \mathbf{m} \) (which is perpendicular to the plane of the loop) and the magnetic field \( \mathbf{B} \) is \( 90^\circ \).

5. **Calculate the Torque**:
- The torque can now be calculated using the formula:
\[ \tau = m \cdot B \cdot \sin(\theta) \]
- Since \( \theta = 90^\circ \), \( \sin(90^\circ) = 1 \):
\[ \tau = m \cdot B \]
- Substituting the expression for \( m \):
\[ \tau = (i \cdot \pi r^2) \cdot B \]
- Thus, the final expression for the magnetic torque is:
\[ \tau = \pi r^2 i B \]

### Final Answer:
The magnetic torque acting on the loop is:
\[ \tau = \pi r^2 i B \]