Figure shows a conducting sphere with a cavity. A point charge `q_(1)` is placed inside cavity, and `q_(2)` is placed out side the sphere `vec(E)_("in")` is electric field due to charge induced on surface of cavity. `vec(E)_("out")` is electric field due to charge induced on outer surface of sphere and `vec(E)_("net")` is net field at any point. Two closed gaussian surface `S_(1)` & `S_(2)` are also drawn in the figure.

Options

A. `int vec(E)_("net").vec(d)a` for surface `S_(1)` is zero
B. `intvec(E)_("net").vec(d)a` for surface `S_(2)` is `(q_(1)+q_(2))/(epsilon_(0))`
C. `int vec(E)_("in").vec(d)a` for surface `S_(1)` is `(-q_(1))/(epsilon_(0))`
D. `int vec(E)_("out").vec(d)a` for surface `S_(2)` is `(q_(1))/(epsilon_(0))`

Answer

A, B, C, D

Explanation

Charge induced on inner surface of cavity `-q_(1)`
Charge induced on outer surface of sphere `=q_(1)`
Net charge enclosed by `S_(1)` is zero
Net charge enclosed by `S_(2)` in `q_(1)+q_(2)`