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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 Cm
Rate of increase of electric field per unit length,
`"dE"/"dl" = 10^-5 "NC"^-1`
Force (F) experienced by the system is given by the relation,
F = qE
`"F" = "q""dE"/"dl" xx "dl"`
= `"p" xx "dE"/"dl"`
= −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 the electric field. Hence, the angle between the electric field and the dipole moment is 180°.
Torque (τ) is given by the relation,
τ = pE sin 180°
= 0
Therefore, the torque experienced by the system is zero.
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