Charge Q1 is inside and charge Q2 is outside a closed surface S. Let E be the electric field at any point on S and phi be the total electric flux through S. Which of the following statements is INCORRECT?

Q1 changes, both E and phi will change.
Q2 changes, E will change but phi will not change.
Q1 = 0 and Q2 ≠ 0 then E ≠ 0 but phi = 0
Q1 ≠ 0 and Q2 = 0 then E = 0 but phi ≠ 0

Correct answer: Q1 ≠ 0 and Q2 = 0 then E = 0 but phi ≠ 0

Solution

Gauss's law gives phi = Q1/epsilon₀, so flux depends only on enclosed charge Q1. However, the electric field E at any point on S is influenced by all charges (Q1 and Q2). Option D claims E = 0 when Q1 ≠ 0 and Q2 = 0, which is false since Q1 itself produces a non-zero field.

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