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.

Answer 1

The correct answer is option 'c'.

Step-by-step explanation:

Gauss's law theoretically can be used to calculate the electric field by any shape of conductor

According to Gauss's law we have

`\oint _s\overrightarrow{E}\cdot \widehat{ds}=(q_(in))/(\epsilon _o)`

Now the integral on the right hand side of the above relation is solved easily if there is a high degree of symmetry in the electric field which is possible in cases when the object is highly symmetric.

The cases of high symmetry include electric fields due to charged spheres, infinite line charge, point charge, infinite plane charged sheet, infinite cylindrical conductor.

But the for the case of limited height of cylinder the symmetry cannot be utilized thus the integral becomes complex to solve, thus cannot be used.