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?

Answer 1

a/c to question, electric field increases in positive z - direction from A to B [see figure ] . so,

electric field at B = electric field at A + electric field gradient × 2a.

or, $E_B=E_A+\frac{dE}{dr}.2a$

or, $E_B-E_A=\frac{dE}{dr}.2a$.....(1)

so, net force on electric dipole will be

$F_{net}=F_B-F_A$

= $q(E_B-E_A)$

from equation (1),

= $q\frac{dE}{dr}.2a$

= $(q.2a)\frac{dE}{dr}$

= $p\frac{dE}{dr}$

given, rate of electric field change , dE/dr = 10^5 N/Cm

and dipole moment, P = 10^-7 Cm

so, F = P dE/dr = (10^-7) × (10^5) = 10^-2 N