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 arbitrary angle to the magnetic field
C. Parallel to the magnetic field
D. Perpendicular to the 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 System**: We have a current-carrying coil placed in a uniform magnetic field. The coil has a magnetic moment (M) due to the current flowing through it.

2. **Magnetic Moment and Area Vector**: The magnetic moment (M) of the coil is given by the product of the current (I) and the area (A) of the coil. The direction of the magnetic moment is perpendicular to the plane of the coil and follows the right-hand rule.

3. **Potential Energy in Magnetic Field**: The potential energy (U) of a magnetic moment in a magnetic field (B) is given by the formula:
\[ U = -\vec{M} \cdot \vec{B} = -MB \cos \theta \]
where \( \theta \) is the angle between the magnetic moment vector and the magnetic field vector.

4. **Minimizing Potential Energy**: The coil will orient itself in such a way as to minimize its potential energy. This occurs when \( \cos \theta \) is maximized, which happens when \( \theta = 0^\circ \) (i.e., when the magnetic moment is parallel to the magnetic field).

5. **Orientation of the Coil**: When the magnetic moment is parallel to the magnetic field, the plane of the coil must be perpendicular to the magnetic field. This is because the area vector (which is perpendicular to the plane of the coil) aligns with the magnetic field.

6. **Conclusion**: Therefore, the current-carrying coil will orient itself such that its plane becomes perpendicular to the uniform magnetic field.

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

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