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 $10^{-7}\, C\, m$ 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

Consider an electric dipole with $-q$ charge at $A$ and $+q$ charge at By placed along $z$-axis, that its dipole moment is in negative $z$ direction. i.e., $p_z = - 10^{-7}\,C\,m$ The electric field is along positive direction of $z$-axis, such that $\frac{d\text{E}}{dz}=10^{5}\,N\,C^{-1}\,m^{-1}$ From $F= qdE=\left(q\times dz\right)\times\frac{dE}{dz}=p \frac{dE}{dz}$ $\therefore F=-10^{-7}\times10^{5}=-10^{-2}\,N$