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Standard XII
Physics
NCERT
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 105NC−1 m−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
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Dipole moment of the system, p=q×dl=−10−7Cm

Rate of increase of electric field per unit length,

dEdl=10+5NC−1

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

F=qE

F=qdEdl×dl

=p×dEdl

=10−7×10−5

=−10−2N

The force is −10−2N in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is 180o.

Torque (τ) is given by the relation,

T=pEsin180o=0

Therefore, the torque experienced by the system is zero.

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