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 ${10}^{5}N{C}^{-1}{m}^{-1}$. The force experienced by the system having a total dipole moment equal to ${10}^{-7}Cm$ in the negative $z-direction$ is

• A. $-{10}^{-2}N$
• B. ${10}^{-2}N$
• C. ${10}^{-4}N$
• D. $-{10}^{-4}N$

Answer 1

The correct option is A $-{10}^{-2}N$

Consider an electric dipole with $-q$ charge at $A$ and $+q$ charge at $B$, placed along z-axis, such that its dipole moment is in negative $z$ direction.
i.e., $P_z={10}^{-7}Cm$
The electric field is along positive direction of z-axis, such that
$\frac{dE}{dz}={10}^{5}N{C}^{-1}{m}^{-1}$
From, $F=qdE$
$=(q\times dz)\times \frac{dE}{dz}=p\frac{dE}{dz}$
Force experienced by the system in the negative z-direction,
$F=p\times (-\frac{dE}{dz})={10}^{-7}\times (-{10}^5)=-{10}^{-2}N$.