The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively

Options

A. `90^(@) and 180^(@)`
B. `0^(@) and 90^(@)`
C. `90^(@) and 0^(@)`
D. `0^(@) and 180^(@)`

Answer

To solve the problem regarding the potential at a point due to an electric dipole and determining the angles at which this potential is maximum and minimum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**:
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance 'd'. The dipole moment (p) is defined as \( p = q \cdot d \).

2. **Potential Due to an Electric Dipole**:
The electric potential \( V \) at a point in space due to an electric dipole is given by the formula:
\[ V = \frac{p \cos \theta}{r^2} \]
where:
- \( p \) is the dipole moment,
- \( \theta \) is the angle between the dipole moment vector and the line joining the dipole to the point,
- \( r \) is the distance from the dipole to the point.

3. **Finding Maximum Potential**:
- The potential \( V \) will be maximum when \( \cos \theta \) is maximum. The maximum value of \( \cos \theta \) is 1, which occurs when \( \theta = 0^\circ \).
- Therefore, the potential is maximum at:
\[ \theta = 0^\circ \]

4. **Finding Minimum Potential**:
- The potential \( V \) will be minimum when \( \cos \theta \) is minimum. The minimum value of \( \cos \theta \) is -1, which occurs when \( \theta = 180^\circ \).
- Therefore, the potential is minimum at:
\[ \theta = 180^\circ \]

5. **Conclusion**:
- The angles at which the potential is maximum and minimum are:
- Maximum potential: \( 0^\circ \)
- Minimum potential: \( 180^\circ \)

### Final Answer:
The potential at a point due to an electric dipole will be maximum when the angle is \( 0^\circ \) and minimum when the angle is \( 180^\circ \).

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