For which of the following charge distributions would Gauss’s law not be useful

Question

For which of the following charge distributions would Gauss’s law not be useful for calculating the electric field?

A. a uniformly charged sphere of radius R

B. a spherical shell of radius R with charge uniformly distributed over its surface

C. a right circular cylinder of radius R and height h with charge uniformly distributed over its surface

D. an infinitely long circular cylinder of radius R with charge uniformly distributed over its surface

E. Gauss’s law would be useful for finding the electric field in all of these cases.

Thanks for any help in advance!

Explanation / Answer

Application of Gauss’s law is limited to systems that possess cylindrical, planar and spherical symmetry. In option C "Cylinder have finite height" so Gauss law is not useful.

The answer for the above question is C

Gauss's law is not useful for calculating the electric field of a right circular cylinder of radius R and height h with charge uniformly distributed over its surface.

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