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Question

# 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?

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Solution

## 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.

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