the angle between of the electric dipolemoment `p` and the electric field `E` when the dipole is in stable equilibrium

Options

A. `0`
B. `pi//4`
C. `pi//2`
D. `pi`

Answer

To determine the angle between the electric dipole moment \( \mathbf{p} \) and the electric field \( \mathbf{E} \) when the dipole is in stable equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Dipole and Torque**:
- An electric dipole consists of two equal and opposite charges separated by a distance. The dipole moment \( \mathbf{p} \) is a vector quantity that points from the negative charge to the positive charge.
- When placed in an electric field \( \mathbf{E} \), the dipole experiences a torque \( \tau \) given by the equation:
\[ \tau = \mathbf{p} \times \mathbf{E} = pE \sin \theta \]
where \( \theta \) is the angle between \( \mathbf{p} \) and \( \mathbf{E} \).

2. **Condition for Equilibrium**:
- For the dipole to be in equilibrium, the net torque acting on it must be zero. This occurs when the dipole moment \( \mathbf{p} \) is aligned with the electric field \( \mathbf{E} \) or directly opposite to it.

3. **Analyzing Angles**:
- The torque is zero when \( \theta = 0^\circ \) (dipole aligned with the field) or \( \theta = 180^\circ \) (dipole anti-aligned with the field). However, we need to determine which of these positions corresponds to stable equilibrium.

4. **Stable vs. Unstable Equilibrium**:
- **Stable Equilibrium**: If the dipole is slightly displaced from its equilibrium position and experiences a restoring torque that brings it back to equilibrium, it is in stable equilibrium. This occurs at \( \theta = 0^\circ \).
- **Unstable Equilibrium**: If the dipole is slightly displaced and experiences a torque that moves it further away from equilibrium, it is in unstable equilibrium. This occurs at \( \theta = 180^\circ \).

5. **Conclusion**:
- Therefore, the angle between the electric dipole moment \( \mathbf{p} \) and the electric field \( \mathbf{E} \) when the dipole is in stable equilibrium is:
\[ \theta = 0^\circ \]