What will be electric potential at any point on the perpendicular bisector of an electric dipole?

Options

A. positive
B. zero
C. Negative
D. None of these

Answer

To find the electric potential at any point on the perpendicular bisector of an electric dipole, we can follow these steps:

### Step 1: Understand the Configuration of the 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 \( p = q \cdot d \). The perpendicular bisector is the line that is equidistant from both charges and is perpendicular to the line joining the two charges.

### Step 2: Identify the Point of Interest
Let’s denote the point where we want to calculate the electric potential as point P, which lies on the perpendicular bisector of the dipole. The distance from each charge to point P will be equal.

### Step 3: Use the Formula for Electric Potential
The electric potential \( V \) at a point due to a dipole is given by the formula:
\[ V = \frac{K \cdot p \cdot \cos(\theta)}{r^2} \]
where:
- \( K \) is the electrostatic constant,
- \( p \) is the dipole moment,
- \( r \) is the distance from the center of the dipole to the point P,
- \( \theta \) is the angle between the dipole moment and the line connecting the dipole to the point P.

### Step 4: Determine the Angle \( \theta \)
At the perpendicular bisector, the angle \( \theta \) between the dipole moment and the line connecting the dipole to point P is 90 degrees. Therefore, \( \cos(90^\circ) = 0 \).

### Step 5: Substitute into the Formula
Substituting \( \theta = 90^\circ \) into the potential formula:
\[ V = \frac{K \cdot p \cdot \cos(90^\circ)}{r^2} = \frac{K \cdot p \cdot 0}{r^2} = 0 \]

### Conclusion
Thus, the electric potential at any point on the perpendicular bisector of an electric dipole is zero.

### Final Answer
The electric potential at any point on the perpendicular bisector of an electric dipole is **0**.

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