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 inversely proportional to ${r^3}$ , for larger $r$ (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

Hint: The electric field around a region can be calculated using Gauss's law. Gauss's law is a general law applicable to any closed surface. It is an important tool because it allows us to estimate the amount of captured charge by mapping the field to the surface outside of the charge distribution. If the geometry is sufficiently symmetrical, the calculation of the electric field can be simplified.

Complete answer:
The current from any enclosed surface is only due to the source (positive charge) and sink (negative charge) of the electric field captured by the surface. Any charge outside the surface does not contribute to the current. If there are different types of charges in a region, but the total charge is zero, then it can be assumed that the region contains multiple electric dipoles. Therefore, at a point outside this area, the dominant electric field is inversely proportional to ${r^3}$ , for larger $r$.

Hence, the correct option is C.

Note: Gauss's law is just a restatement of Coulomb's law. If Gauss's theorem is applied to a point charge surrounded by a sphere, Coulomb's law can be easily obtained. In addition, only electric charges can be used as the source or sink of the electric field. For example, changing magnetic fields cannot be used as sources or sinks of electric fields.