When a current carrying coil is placed in a uniform magnetic field with its magnetic moment anti-parallel to the field.

Options

A. torque on it is maximum
B. torque on it is zero
C. potential energy is maximum
D. dipole is in unstable equilibrium

Explanation

To solve the problem of a current-carrying coil placed in a uniform magnetic field with its magnetic moment anti-parallel to the field, we can follow these steps:

### Step 1: Understand the Configuration
When a current-carrying coil is placed in a magnetic field, it experiences a torque due to the interaction between the magnetic moment of the coil and the magnetic field. The magnetic moment (\( \vec{m} \)) is defined as \( \vec{m} = NIA \hat{n} \), where \( N \) is the number of turns, \( I \) is the current, \( A \) is the area of the coil, and \( \hat{n} \) is the unit vector normal to the plane of the coil.

**Hint:** Identify the direction of the magnetic moment and the magnetic field.

### Step 2: Determine the Torque
The torque (\( \vec{\tau} \)) experienced by the coil in a magnetic field (\( \vec{B} \)) is given by the formula:
\[ \vec{\tau} = \vec{m} \times \vec{B} \]
Since the magnetic moment is anti-parallel to the magnetic field, the angle (\( \theta \)) between \( \vec{m} \) and \( \vec{B} \) is \( 180^\circ \). The magnitude of the torque can be calculated as:
\[ |\tau| = mB \sin(\theta) \]
At \( \theta = 180^\circ \), \( \sin(180^\circ) = 0 \), thus:
\[ |\tau| = mB \cdot 0 = 0 \]

**Hint:** Remember that the sine of \( 180^\circ \) is zero, leading to zero torque.

### Step 3: Analyze Potential Energy
The potential energy (\( U \)) of a magnetic dipole in a magnetic field is given by:
\[ U = -\vec{m} \cdot \vec{B} = -mB \cos(\theta) \]
Substituting \( \theta = 180^\circ \):
\[ U = -mB \cos(180^\circ) = -mB \cdot (-1) = mB \]
This indicates that the potential energy is at a maximum when the magnetic moment is anti-parallel to the magnetic field.

**Hint:** The cosine of \( 180^\circ \) is negative, which flips the sign of the potential energy.

### Step 4: Determine Stability
When the potential energy is at a maximum and the torque is zero, the system is in an unstable equilibrium. This means that any small displacement will result in a force that tends to move the dipole further away from this position.

**Hint:** Recognize that maximum potential energy corresponds to unstable equilibrium.

### Conclusion
In summary, when a current-carrying coil is placed in a uniform magnetic field with its magnetic moment anti-parallel to the field:
- The torque on the coil is zero.
- The potential energy is at a maximum.
- The system is in an unstable equilibrium.

Thus, the correct option regarding the behavior of the coil in this configuration is that the torque is zero and the potential energy is maximum, indicating unstable equilibrium.