A magentic dipole in a constant magnetic field has

Options

A. maximum potential energy when the torque is maximum
B. zero potential energy when the torque is maximum
C. zero potential energy when the torque is minimum
D. minimum potential energy when the torque is maximum

Answer

To solve the question regarding the relationship between the potential energy and torque of a magnetic dipole in a constant magnetic field, we will follow these steps:

### Step 1: Understand the Definitions
- The magnetic dipole moment is represented as **P**.
- The magnetic field is represented as **E**.
- The angle between the magnetic dipole moment and the magnetic field is represented as **θ**.

### Step 2: Write the Formula for Potential Energy
The potential energy (**U**) of a magnetic dipole in a magnetic field is given by the formula:
\[ U = -\mathbf{P} \cdot \mathbf{E} = -PE \cos \theta \]
where:
- **U** is the potential energy,
- **P** is the magnetic dipole moment,
- **E** is the magnetic field strength,
- **θ** is the angle between **P** and **E**.

### Step 3: Write the Formula for Torque
The torque (**τ**) experienced by a magnetic dipole in a magnetic field is given by:
\[ \tau = \mathbf{P} \times \mathbf{E} = PE \sin \theta \]
where:
- **τ** is the torque,
- **P** is the magnetic dipole moment,
- **E** is the magnetic field strength,
- **θ** is the angle between **P** and **E**.

### Step 4: Analyze the Options
1. **Maximum Potential Energy when Torque is Maximum**:
- Torque is maximum when **θ = 90°** (since sin 90° = 1).
- At **θ = 90°**, potential energy becomes:
\[ U = -PE \cos(90°) = -PE \cdot 0 = 0 \]
- Thus, potential energy is not maximum when torque is maximum. **This option is incorrect.**

2. **0 Potential Energy when Torque is Maximum**:
- As established, torque is maximum when **θ = 90°**, leading to:
\[ U = 0 \]
- Therefore, this statement is true. **This option is correct.**

### Conclusion
The correct answer is that the potential energy is zero when the torque is maximum.

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