five charge `q_(1),q_(2),q_(3),q_(4)`and `q_(5)` are fixed at their positions as shown in figure .`s` is Gaussian surface .The Gauss's law is given by `ointvec(E).vec(ds)=(q)/(epsilon_(0))`

Which of the following statement is correct?

Options

A. E on the LHS of the above equation will have a contribution from `q_(1),q_(5) and q_(1),q_(5)` and `q_(3)` while q on the RHS will have a contribution from `q_(2) and q_(4)` only.
B. E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from `q_(2) and q_(4)` only.
C. E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from `q_(1),q_(3) and q_(5)` only
D. Both E on the LHS and q on the RHS will have contributions from `q_(2) and q_(4) ` only.

Answer

B

Explanation

According to Gauss' law, the term q on the right side of the equation `int_(S).E.dS=(q)/(epsi_(0))` includes the sum of all charges enclosed by the surface.
The charges may be located anywhere inside the surface, if the surface is so chosen that there are some charges inside and some outside, the electric field on the left side of equaiton is due to all the charges, both inside and outside S.
So, E on LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from `q_(2) and q_(4)` only.