Electric Dipole

Given:

• An infinite cylinder with positive uniform charge density
• An electric dipole made of charges and , connected by a massless rod
• The dipole is placed such that the two charges are at different distances from the axis

Electric field inside the cylinder:

The electric field at a distance from the axis is given by:

This means the field is radially outward and increases with .

Effect on the dipole:

• The charge is farther from the axis, so it experiences a stronger force outward.
• The charge is closer, so it experiences a weaker inward force.
• Thus, there is a net force to the right (outward).
• The forces form a couple (since they are not collinear), causing a clockwise torque.

Conclusion:

The dipole experiences a force to the right and a clockwise torque.

Correct option: (B): a force to the right and a clockwise torque

Given:
An electric dipole with dipole moment produces an electric field at a point on the x-axis, making an angle with the axis.

Using the identity:
, and

Electric Field Components:
Resolving the electric field into components:
⟶ (1)
⟶ (2)

Dividing (2) by (1):

Also given:

After simplification and solving, the resulting expression for potential energy is:
Answer:

Correct Option: (D)