An electric dipole is kept in non-unifrom electric field. It experiences

Options

A. a force and a torque
B. a force but not a torque
C. a torque but not a force
D. Neither a force nor a torque

Answer

To solve the problem of an electric dipole placed in a non-uniform electric field, we need to analyze the forces and torques acting on the dipole. Here’s a step-by-step solution:

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance \(d\). The dipole moment \( \vec{p} \) is defined as:
\[ \vec{p} = q \cdot \vec{d} \]
where \( \vec{d} \) is the vector pointing from the negative charge to the positive charge.

### Step 2: Identify the Electric Field
In a non-uniform electric field, the electric field strength varies from one point to another. Let’s denote the electric field at the position of the positive charge as \( \vec{E_1} \) and at the position of the negative charge as \( \vec{E_2} \).

### Step 3: Calculate the Forces on Each Charge
The force experienced by the positive charge (+q) in the electric field \( \vec{E_1} \) is:
\[ \vec{F_1} = q \cdot \vec{E_1} \]
The force experienced by the negative charge (-q) in the electric field \( \vec{E_2} \) is:
\[ \vec{F_2} = -q \cdot \vec{E_2} \]

### Step 4: Determine the Net Force on the Dipole
Since \( \vec{E_1} \) and \( \vec{E_2} \) are not equal (due to the non-uniformity of the electric field), the net force \( \vec{F}_{net} \) acting on the dipole is:
\[ \vec{F}_{net} = \vec{F_1} + \vec{F_2} = q \cdot \vec{E_1} - q \cdot \vec{E_2} \]
Since \( \vec{E_1} \neq \vec{E_2} \), \( \vec{F}_{net} \) is non-zero, indicating that the dipole experiences a net force.

### Step 5: Calculate the Torque on the Dipole
The torque \( \vec{\tau} \) acting on the dipole due to these forces can be calculated. The torque due to the force \( \vec{F_1} \) is given by:
\[ \vec{\tau_1} = \vec{r_1} \times \vec{F_1} \]
and the torque due to the force \( \vec{F_2} \) is:
\[ \vec{\tau_2} = \vec{r_2} \times \vec{F_2} \]
where \( \vec{r_1} \) and \( \vec{r_2} \) are the position vectors from the pivot point to the points where the forces are applied.

### Step 6: Determine the Net Torque
The total torque \( \vec{\tau}_{net} \) on the dipole is the sum of the individual torques:
\[ \vec{\tau}_{net} = \vec{\tau_1} + \vec{\tau_2} \]
Since both \( \vec{\tau_1} \) and \( \vec{\tau_2} \) are not zero, the dipole experiences a net torque.

### Conclusion
In a non-uniform electric field, an electric dipole experiences both a net force and a net torque. Therefore, the correct answer is that the dipole experiences both force and torque.