A current carrying coil is subjected to a uniform magnetic field. The coil will orient so that its plane become

Options

A. inclined at `45^(@)` to the magnetic field
B. inclined at any arbitary angle to the magnetic field
C. parallel to the magnetic field
D. perpendicular to magnetic field

Answer

To solve the question regarding the orientation of a current-carrying coil in a uniform magnetic field, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Setup**:
- We have a current-carrying coil placed in a uniform magnetic field. The coil has a certain plane, and we need to determine how it will orient itself in the presence of the magnetic field.

2. **Direction of Current and Magnetic Field**:
- Assume the coil has a current flowing through it in a specific direction. Let's denote the direction of the magnetic field as \( \vec{B} \).

3. **Applying the Right-Hand Rule**:
- To find the direction of the force acting on the coil, we can use the right-hand rule. For a segment of the coil carrying current \( I \), the force \( \vec{F} \) on that segment can be calculated using the formula:
\[ \vec{F} = I \vec{L} \times \vec{B} \]
- Here, \( \vec{L} \) is the length vector of the current element.

4. **Analyzing Forces on Different Segments**:
- For segments of the coil where the current flows in the same direction as the magnetic field, the force will be zero (since \( \sin(0) = 0 \)).
- For segments where the current flows in the opposite direction to the magnetic field, the force will also be zero (since \( \sin(180) = 0 \)).
- For segments perpendicular to the magnetic field, the force will be maximum.

5. **Resulting Torque**:
- The forces on opposite sides of the coil will create a torque about the axis of the coil. This torque will tend to rotate the coil.

6. **Equilibrium Position**:
- The coil will continue to rotate until it reaches a position where the torque is zero. This occurs when the plane of the coil is perpendicular to the magnetic field lines.

7. **Conclusion**:
- Therefore, the coil will orient itself such that its plane becomes perpendicular to the direction of the uniform magnetic field.

### Final Answer
The coil will orient itself so that its plane becomes **perpendicular to the magnetic field**.

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