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Asked in RS Academy GUJCET booklet · Gauss's law and enclosed charge
Given: a closed surface first encloses a charge of 10 μC and the flux through it is φ; a charge of -10 μC is then placed inside the same surface.
Idea: Gauss's law says the flux through a closed surface depends only on the algebraic sum of the charges it encloses, φ = (q_enc)/(ε₀). Where those charges sit inside, and what charges lie outside, make no difference.
First case: q_enc = 10 μC, giving the flux φ.
After the second charge: q_enc = 10 + (-10) = 0 μC.
So the flux becomes 0/(ε₀), that is zero.
The field on the surface is not zero everywhere - it is strong near each charge - but as much of it points inward as outward, so the net flux is zero.
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