Question

A positive charge q is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance $\overrightarrow{l}$. Force on charge q is:

• A. in the direction parallel to vector $\overrightarrow{l}$
• B. in radial direction
• C. in a direction which depend on the magnitude of charge density in sphere
• D. direction can not be determined

Answer 1

Answer: (A), (B)

The correct options are
A in the direction parallel to vector $\overrightarrow{l}$
B in radial direction

Since, sphere is uniformly charged therefore, charge distributed at a distance $x>l$ will have no effect on the charge particle. Since by applying gauss's law we find that electric field at $x=l$ due to charge present in sphere at $x>l$ will be zero. Therefore, no effect due to that charge.
Now , only electric field present or acting on the charge particle will be due to charge lying in the region $0<x<l$ and that field will be radially outwards and in the direction of $\overrightarrow{l}$ therefore, $F=qE$ therefore, direction of the force is also same in the same direction.
Therefore, option(A), (B)