A short bar magnet of magnetic moment `0*4JT^-1` is placed in a uniform magnetic field of `0*16T`. The magnet is in stable equilibrium when the potencial energy is

Options

A. 0.064 J
B. `-0.064 J`
C. Zero
D. `-0.082 J`

Explanation

To solve the problem, we need to find the potential energy of a short bar magnet placed in a uniform magnetic field when it is in stable equilibrium.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Magnetic moment (m) = 0.4 JT⁻¹
- Magnetic field (B) = 0.16 T

2. **Understand the Formula for Potential Energy**:
The potential energy (U) of a magnetic moment in a magnetic field is given by the formula:
\[ U = -\vec{m} \cdot \vec{B} = -mB \cos \theta \]
where:
- \( \vec{m} \) is the magnetic moment,
- \( \vec{B} \) is the magnetic field,
- \( \theta \) is the angle between the magnetic moment and the magnetic field.

3. **Determine the Angle for Stable Equilibrium**:
For stable equilibrium, the angle \( \theta \) should be 0 degrees. This means that the magnetic moment is aligned with the magnetic field.

4. **Calculate the Potential Energy**:
Since \( \theta = 0^\circ \), we have:
\[ \cos(0^\circ) = 1 \]
Thus, the potential energy becomes:
\[ U = -mB \cos(0^\circ) = -mB \]
Substituting the values:
\[ U = - (0.4 \, \text{JT}^{-1}) \times (0.16 \, \text{T}) \]
\[ U = -0.064 \, \text{J} \]

5. **Final Answer**:
The potential energy when the magnet is in stable equilibrium is:
\[ U = -0.064 \, \text{J} \]