. 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 per metre. What are the force and torque experienced by a system having a total dipole moment equal to Cm in the negative z-direction?
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Answer:
Dipole moment of the system, p=q×dl=−10
−7
Cm
Rate of increase of electric field per unit length,
dl
dE
=10
+5
NC
−1
Force (F) experienced by the system is given by the relation,
F=qE
F=q
dl
dE
×dl
=p×
dl
dE
=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
o
.
Torque (τ) is given by the relation,
T=pEsin180
o
=0
Therefore, the torque experienced by the system is zero.
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