In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC−1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10−7 Cm in the negative z-direction?

Question 1.27: In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10⁵ NC⁻¹ per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10⁻⁷ Cm in the negative z-direction?

Answer:

Method - 1

 Dipole moment of the system, p = q × dl = −10⁻⁷ C m Rate of increase of electric field per unit length,

 Force (F) experienced by the system is given by the relation,

F = qE

 = −10⁻⁷ × 10⁻⁵ = −10⁻² N

The force is −10⁻² N in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is 180°. Torque (τ) is given by the relation,

 τ = pE sin180° = 0

 Therefore, the torque experienced by the system is zero.

 Method - 2