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

Options

A. the electric field is necessarily zero.
B. The electric field is due to the dipole moment of the cahrge distribution only.
C. The dominant electric field is `prop(1)/(r_(3))`, for large r, where r is the distance from a origin in this regions.
D. the work done to move a charged particle along a closed path, away from the region, will be zero.

Answer

C, D

Explanation

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 (may be anywhere w.r.t. electric dipoles) the dominant electric field `prop(1)/(r_(3))` for large r.
Further, as electric field is conservative, work done to move a charged particle along a closed path, away from the region will be zero.