A current carrying circular coil, suspended freely in a uniform external magnetic field orients to a position of stable equilibrium. In this state :

Options

A. The plane of coil is normal to external magnetic field
B. The plane of coil is parallel to external magnetic field
C. Flux through coil is minimum
D. Torque on coil is maximum

Answer

To solve the problem regarding the orientation of a current-carrying circular coil suspended in a uniform external magnetic field at stable equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a circular coil carrying a current \( I \) and it is suspended in a uniform magnetic field \( \vec{B} \). The coil can rotate freely.

2. **Conditions for Stable Equilibrium**:
- For the coil to be in stable equilibrium, the net torque \( \tau \) acting on it must be zero. This means that the coil does not tend to rotate further in any direction.

3. **Torque on the Coil**:
- The torque \( \tau \) on the coil can be expressed as:
\[ \tau = \vec{m} \times \vec{B} \]
where \( \vec{m} \) is the magnetic moment of the coil, given by:
\[ \vec{m} = I \cdot A \]
Here, \( A \) is the area vector of the coil, which is perpendicular to the plane of the coil.

4. **Angle Between Vectors**:
- The angle \( \theta \) between the magnetic moment \( \vec{m} \) and the magnetic field \( \vec{B} \) is crucial. The torque can also be expressed as:
\[ \tau = mB \sin \theta \]
- For the torque to be zero, \( \sin \theta \) must be zero. This occurs when \( \theta = 0^\circ \) or \( \theta = 180^\circ \), meaning that the magnetic moment \( \vec{m} \) is either parallel or anti-parallel to the magnetic field \( \vec{B} \).

5. **Conclusion on Orientation**:
- When \( \theta = 0^\circ \), the plane of the coil is normal (perpendicular) to the magnetic field. This is the condition for stable equilibrium. If the plane of the coil were parallel to the magnetic field, the torque would not be zero, and the coil would not be in stable equilibrium.

6. **Evaluating the Options**:
- **Option A**: The plane of the coil normal to the external magnetic field - **Correct**.
- **Option B**: The plane of the coil parallel to the external magnetic field - **Incorrect**.
- **Option C**: Flux through the coil is minimum - **Incorrect** (the flux is maximum when the plane is normal to the field).
- **Option D**: Torque on the coil is maximum - **Incorrect** (the torque is zero in stable equilibrium).

### Final Answer:
The correct statement is that the plane of the coil is normal to the external magnetic field.

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