An electric dipole has the magnitude of its charge as `q` and its dipole moment is `p`. It is placed in a uniform electric field `E`. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively
(a) `2qE` and minimum (b) `qE` and `pE`
(c) zero and minimum (d) qE and maximum

Options

A. `2qE` and minimum
B. `qE` and `pE`
C. zero and minimum
D. qE and maximum

Answer

To solve the problem regarding the electric dipole in a uniform electric field, we will analyze the forces acting on the dipole and its potential energy step by step.

### Step 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:
\[ p = q \cdot d \]
In this case, we are given that the dipole moment is \( p \) and the magnitude of the charge is \( q \).

### Step 2: Analyzing the Forces on the Dipole
When an electric dipole is placed in a uniform electric field \( E \), the forces acting on the positive and negative charges are equal in magnitude but opposite in direction.

- The force on the positive charge (+q) is:
\[ F_+ = qE \]
- The force on the negative charge (-q) is:
\[ F_- = -qE \]

### Step 3: Calculating the Net Force
The net force \( F_{net} \) on the dipole is the vector sum of the forces acting on the positive and negative charges:
\[ F_{net} = F_+ + F_- = qE - qE = 0 \]
Thus, the net force acting on the dipole is zero.

### Step 4: Calculating the Potential Energy
The potential energy \( U \) of an electric dipole in a uniform electric field is given by the formula:
\[ U = -\vec{p} \cdot \vec{E} = -pE \cos \theta \]
where \( \theta \) is the angle between the dipole moment \( \vec{p} \) and the electric field \( \vec{E} \).

In this case, since the dipole moment is along the direction of the electric field, \( \theta = 0^\circ \):
\[ U = -pE \cos(0) = -pE \]
This value is negative, indicating that the potential energy is at a minimum when the dipole is aligned with the electric field.

### Conclusion
From our analysis, we find that:
- The net force on the dipole is **zero**.
- The potential energy of the dipole is **minimum**.

Thus, the correct answer is:
**(c) zero and minimum.**