The electrostatic potnetial due to an electric dipole at an equatorial point is

Options

A. maximum
B. zero
C. minimum
D. not defined

Answer

To find the electrostatic potential due to an electric dipole at an equatorial point, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration of the Dipole:**
- An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance of 2a. The midpoint between the charges is denoted as point O.

2. **Identify the Equatorial Point:**
- The equatorial point is located at a distance R from the midpoint O, along the perpendicular bisector of the dipole.

3. **Calculate the Potential due to +q:**
- The potential (V) at point A due to the positive charge +q is given by the formula:
\[ V_{+q} = \frac{kq}{d_{+q}} \]
- Here, \(d_{+q}\) is the distance from the charge +q to point A. By applying the Pythagorean theorem, we find:
\[ d_{+q} = \sqrt{R^2 + a^2} \]
- Therefore, the potential due to +q becomes:
\[ V_{+q} = \frac{kq}{\sqrt{R^2 + a^2}} \]

4. **Calculate the Potential due to -q:**
- Similarly, the potential at point A due to the negative charge -q is:
\[ V_{-q} = \frac{k(-q)}{d_{-q}} \]
- The distance \(d_{-q}\) is also:
\[ d_{-q} = \sqrt{R^2 + a^2} \]
- Thus, the potential due to -q is:
\[ V_{-q} = \frac{-kq}{\sqrt{R^2 + a^2}} \]

5. **Calculate the Total Potential at Point A:**
- The total potential \(V\) at point A due to both charges is the sum of the potentials:
\[ V = V_{+q} + V_{-q} \]
- Substituting the values we calculated:
\[ V = \frac{kq}{\sqrt{R^2 + a^2}} + \frac{-kq}{\sqrt{R^2 + a^2}} \]
- This simplifies to:
\[ V = 0 \]

### Conclusion:
The electrostatic potential due to an electric dipole at an equatorial point is **0**.