Question

Consider a region inside which, there are various types of charges but the total charge is zero. At points outside the region

• A. the electric field is necessarily zero
• B. the electric field is due to the dipole moment of the charge distribution only
• C. the dominant electric field is inversely proportional to $r^3$, for large $r$ (distance from origin)
• D. the work done to move a charged particle along a closed path, away from the region will not be zero

Answer 1

Answer: (C)

When there are various types of charges in a region, but the total charge is zero, the region can be supposed to contain a number of electric dipoles. Therefore, at points outside the region, the dominant electric field $\propto \frac{1}{r^{3}}$ for large $r$.