Question

For an electric dipole in a non-uniform electric field with dipole moment parallel to the direction of the field, the force F and torque τ on the dipole respectively are______.
Fill in the blank with the correct answer from the options given below.

• A. F = 0, τ = 0
• B. F ≠ 0, τ = 0
• C. F = 0, τ ≠ 0
• D. F ≠ 0, τ ≠ 0

Answer 1

The Correct Option is B

An electric dipole within an electric field experiences both forces and torques due to their interaction. Let's examine these scenarios:

Force (F) on the Dipole: In a non-uniform electric field, the force exerted on a dipole is typically non-zero. This is because the electric field's strength varies across different spatial locations, resulting in a net force acting on the dipole.

Torque (τ) on the Dipole: The torque acting on a dipole is contingent upon the angle between its dipole moment (p) and the electric field (E). The torque τ is quantified as:

\(τ = pE sin θ\)

Here, θ represents the angle between the dipole moment and the electric field. When the dipole moment is aligned parallel to the electric field, θ equals 0, consequently making sin θ = 0. This leads to:

\(τ = 0\)

Conclusion: For a dipole situated in a non-uniform electric field with its dipole moment parallel to the field, the force F is non-zero (F ≠ 0), whereas the torque τ is zero (τ = 0).

Correct Answer: \(F ≠ 0, τ = 0\)