An electric dipole is placed in a uniform electric field. It may experience

Options

A. A force only
B. A torque only
C. Both force and torque
D. neither torque nor force

Answer

To solve the question regarding the behavior of an electric dipole placed in a uniform electric field, we will analyze the forces and torques acting on the dipole step by step.

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance \(2a\). The dipole moment \( \vec{p} \) is given by:
\[ \vec{p} = q \cdot 2a \]
The dipole has a positive charge on one end and a negative charge on the other.

### Step 2: Define the Electric Field
A uniform electric field \( \vec{E} \) is defined as a field that has the same magnitude and direction at all points in space. The force \( \vec{F} \) on each charge in the dipole due to the electric field can be calculated as:
\[ \vec{F}_+ = q \vec{E} \quad \text{(on the positive charge)} \]
\[ \vec{F}_- = -q \vec{E} \quad \text{(on the negative charge)} \]

### Step 3: Calculate the Net Force
The net force \( \vec{F}_{net} \) on the dipole is the vector sum of the forces acting on the positive and negative charges:
\[ \vec{F}_{net} = \vec{F}_+ + \vec{F}_- = q \vec{E} - q \vec{E} = 0 \]
Thus, the net force acting on the dipole in a uniform electric field is zero.

### Step 4: Calculate the Torque
Torque \( \vec{\tau} \) acting on the dipole can be calculated about the center of the dipole. The torque due to the forces acting on the dipole is given by:
\[ \vec{\tau} = \vec{r} \times \vec{F} \]
Where \( \vec{r} \) is the position vector from the center of the dipole to the point of application of the force. The torque due to the forces on the dipole can be expressed as:
\[ \tau = pE \sin(\theta) \]
Where \( \theta \) is the angle between the dipole moment \( \vec{p} \) and the electric field \( \vec{E} \).

### Step 5: Analyze the Conditions
1. If the dipole is aligned with the electric field (i.e., \( \theta = 0^\circ \)), the torque is zero, and the dipole is in stable equilibrium.
2. If the dipole is not aligned (i.e., \( \theta \neq 0^\circ \)), a torque will act to align the dipole with the electric field.

### Conclusion
In a uniform electric field, an electric dipole experiences:
- **Zero net force** (since the forces on the charges cancel each other).
- **Torque** that tends to align the dipole with the electric field.

Thus, the correct answer to the question is that the electric dipole may experience **torque only**.