Question

If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Suppose now that Coulomb's force between two charges varies as $1/r^3$. Then, for a charged solid metallic sphere

• A. field inside will be zero and charge density inside will be zero
• B. field inside will not be zero and charge density inside will not be zero
• C. field inside will not be zero and charge density inside will be zero
• D. field inside will be zero and charge density inside will not be zero

Answer 1

Answer: (D)

field inside will be zero and charge density inside will not be zero

Here density is varying with respect to radius means in any volume it has some charge so charge density will not be zero.

But if you consider any point suppose A, then it has A' opposite to it causing net field $E+E_1=0$