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. `vecE` on the LHS of the above equation will have a contribution from `q_1,q_2` and `q_3` while q on the RHS will have a contribution from `q_2` and `q_4` only.
B. `vecE` 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. `vecE` 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 `vecE` on the LHS and q on the RHS will have contributions from `q_2` and `q_4` only.

Answer

B

Explanation

We know that Gauss.s law can be written as :
`oint_"closed surface" vecE . dvecS=q_"in"/epsilon_0`
In this equation electric field intensity `vecE` on the Gaussian surface is net electric field intensity due to all charges whether inside or outside the surface. Here, Gauss.s theorem says that surface integral of net electric field for complete surface depends only on the net charge enclosed within the Gaussian surface.
Thus, `vecE` in the LHS of given equation is due to all the charges and the q on the RHS of the above equation will have contribution from `q_2` and `q_4` only.