Inside a ball charged uniformly with volume density `rho` there is a spherical cavity. The centre of the ball by a distance `a`. Find the field strength `E` inside the cavity, assuming the permittively equal to unity.

Options

A. `0`
B. `(pa)/(2epsilon_(0))`
C. `(pa)/(3epsilon_(0))`
D. `(pa)/(epsilon_(0))`

Answer

A

Explanation

Electric field at any point inside the cavity= Electric field due to entire sphere at that point =the field at the same point due to a solid sphere which can tightly fit into the cavity

`vec(E)=vec(E)_(1)-vec(E)_(2)` According to Gauss's law
`vec(E)_(1)=(p)/(3epsilon_(0))r_(1) vec(E)=(p)/(3epsilon_(0))(vec(r)_(1)-vec(r)_(2))`
`vec(E)_(2)=(p)/(3epsilon_(0))r_(2) vec(E)=(p)/(3epsilon_(0))vec(a)( :.vec(a)=vec(r)_(1)-vec(r)_(2))`