Class-12th Physics, CBSE and UP Board
Electric Charges and Fields,
Chapter-1, Exercise -1, Additional Exercise, Q-1.27
NCERT Solutions for Class 12th Physics
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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Dipole moment of the system, p=q x dl =10⁻⁷Cm
Rate of increase of electric field per unit length dE/dl =105 NC_1
Force (F) experienced by the system is given by the relation,
F = qE = q x (dE/dl) x dl = q x dl x (dE/dl) = p x (dE/dl)
= —1(10⁻7 x 105 )= —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 sinl80° = 0
Therefore, the torque experienced by the system is zero.