At a point on the axis (but not inside the dipole and not at infinity) of an electric dipole

Options

A. The electric field is zero
B. The electric potential is zero
C. Neither the electric field not the electric potential is zero
D. The electric field is directed perpendicular to the axis of the dipole

Answer

To solve the problem regarding the electric field and electric potential at a point on the axis of an electric dipole, we can follow these steps:

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges separated by a distance \(2a\). The dipole moment \(p\) is defined as:
\[ p = q \cdot 2a \]
where \(q\) is the magnitude of one of the charges.

### Step 2: Identify the Point of Interest
The question specifies that we are looking at a point on the axis of the dipole, but not inside the dipole and not at infinity. This means we are considering a point along the line extending from the positive charge to the negative charge.

### Step 3: Electric Field on the Axis of the Dipole
The electric field \(E\) at a distance \(r\) from the center of the dipole along the axis is given by the formula:
\[ E = \frac{2kp}{r^3} \]
where \(k\) is Coulomb's constant and \(p\) is the dipole moment.

### Step 4: Electric Potential on the Axis of the Dipole
The electric potential \(V\) at a distance \(r\) from the dipole along the axis is given by:
\[ V = \frac{k p}{r^2} \]

### Step 5: Evaluate the Conditions
- Since the point is not at infinity, both the electric field and potential will not be zero.
- The electric field points away from the positive charge and towards the negative charge along the axis.

### Step 6: Conclusion
Based on the above analysis, we can conclude:
- The electric field at the point is given by \(E = \frac{2kp}{r^3}\).
- The electric potential at the point is given by \(V = \frac{kp}{r^2}\).
- Since the point is not at infinity, both \(E\) and \(V\) will have non-zero values.

### Final Answer
The correct option regarding the electric field and potential at a point on the axis of an electric dipole (not inside and not at infinity) is **C**.

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