Force on current carrying loop (Radius = R) in uniform magnetic (B) field which is at an angle 30” with the normal will be :-

Options

A. zero
B. `2piRiB`
C. `2sqrt3piRiB`
D. `piRiB`

Explanation

To solve the problem of finding the force on a current-carrying loop of radius \( R \) in a uniform magnetic field \( B \) that is at an angle of \( 30^\circ \) with the normal to the plane of the loop, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a circular loop of radius \( R \) carrying a current \( I \).
- The loop is placed in a uniform magnetic field \( B \) which makes an angle of \( 30^\circ \) with the normal to the plane of the loop.

2. **Magnetic Force on a Current-Carrying Loop**:
- The magnetic force \( \mathbf{F} \) on a current-carrying conductor in a magnetic field is given by the formula:
\[ \mathbf{F} = I (\mathbf{L} \times \mathbf{B}) \]
- For a closed loop, the net force can be calculated using the magnetic moment \( \mathbf{m} \) of the loop.

3. **Magnetic Moment**:
- The magnetic moment \( \mathbf{m} \) of the loop is given by:
\[ \mathbf{m} = I \cdot A \]
- Where \( A \) is the area of the loop. For a circular loop:
\[ A = \pi R^2 \]
- Thus,
\[ \mathbf{m} = I \cdot \pi R^2 \]

4. **Torque on the Loop**:
- The torque \( \tau \) experienced by the loop in the magnetic field is given by:
\[ \tau = \mathbf{m} \cdot \mathbf{B} = mB \cos(\theta) \]
- Here, \( \theta \) is the angle between \( \mathbf{m} \) and \( \mathbf{B} \). In this case, \( \theta = 30^\circ \).

5. **Force Calculation**:
- However, the key point is that the net force on a closed current-carrying loop in a uniform magnetic field is zero. This is because the forces on opposite sides of the loop cancel each other out.
- Therefore, regardless of the angle, the total force \( \mathbf{F}_{net} = 0 \).

6. **Conclusion**:
- Hence, the force on the current-carrying loop in the uniform magnetic field at an angle of \( 30^\circ \) with the normal is:
\[ \mathbf{F} = 0 \]

### Final Answer:
The force on the current-carrying loop in the uniform magnetic field is **0**.