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^(@)`

Explanation

To determine the angles at which the electric potential due to an electric dipole is maximum and minimum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Dipole Potential**:
The electric potential \( V \) at a point due to an electric dipole is given by the formula:
\[ V = \frac{1}{4\pi \epsilon_0} \cdot \frac{\mathbf{p} \cdot \hat{r}}{r^2} \]
where \( \mathbf{p} \) is the dipole moment, \( \hat{r} \) is the unit vector in the direction from the dipole to the point of interest, and \( r \) is the distance from the dipole to the point.

2. **Identifying the Angle**:
The angle \( \theta \) is defined as the angle between the dipole moment vector \( \mathbf{p} \) and the line joining the dipole to the point where the potential is being calculated.

3. **Maximum Potential**:
The potential is maximum when \( \cos \theta = 1 \), which occurs at:
\[ \theta = 0^\circ \]
At this angle, the potential is:
\[ V_{\text{max}} = \frac{p}{4\pi \epsilon_0 r^2} \]

4. **Minimum Potential**:
The potential is minimum when \( \cos \theta = -1 \), which occurs at:
\[ \theta = 180^\circ \]
At this angle, the potential is:
\[ V_{\text{min}} = -\frac{p}{4\pi \epsilon_0 r^2} \]

5. **Zero Potential**:
The potential is zero when \( \cos \theta = 0 \), which occurs at:
\[ \theta = 90^\circ \]
At this angle, the potential is:
\[ V = 0 \]

### Final Answer:
- The potential at a point due to an electric dipole is maximum when \( \theta = 0^\circ \) and minimum when \( \theta = 180^\circ \). The potential is zero when \( \theta = 90^\circ \).