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Question

Charge Q1 and Q2 lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and ϕ be the flux of E over S.

A
If Q1 changes, both E and ϕ will change
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B
If Q2 changes, E will change but ϕ will not change
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C
If Q1 = 0 and Q2 0 then E 0 but ϕ = 0
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D
If Q1 0 and Q2 = 0 then E = 0 but ϕ 0
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Solution

The correct options are
A If Q1 changes, both E and ϕ will change
B If Q2 changes, E will change but ϕ will not change
D If Q1 = 0 and Q2 0 then E 0 but ϕ = 0
As the electric field at any point on surface S is the resultant effect due to all charges in the system, so field at any point on S is E=E1+E2 where E1 is the field due to Q1 and E2 is the field due to Q2
Applying Gauss's law, the flux over S , ϕ=Qenϵ0 where Qen=Q1= charge enclosed by S.
Thus field depends on both charges but flux is only depends on the charges Q1.
So according to this the options A,B and C will be correct.

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