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Consider a region inside which there are various types

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 ∝ 1/r3  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

Solution:

Here, net charge is zero in the region. We can assume that contain one or more than one electric dipoles.

So, at points outside the region, the dominant electric field for ∝ 1/r3 for large r.

Also, electric field is conservative field, work done to move a charged particle along a closed path, away from the region will be zero.

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