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Statement 1: A charge lies outside a Gaussian sphere of radius R; therefore the electric field on the surface of the sphere is zero. Statement 2: Since the closed surface integral of E over area equals q_enclosed/e0 and q_enclosed = 0 for this sphere, the integral of E dot dS over the surface is zero. Choose the correct option.

1. Statement-1 is true, statement-2 is true and statement-2 is the correct explanation for statement-1.
2. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
3. Statement-1 is true, statement-2 is false.
4. Statement-1 is false, statement-2 is true.

Correct answer: Statement-1 is false, statement-2 is true.

Solution

Statement 2 is correct: with no enclosed charge the net flux is zero. But Statement 1 is wrong: the external charge produces a non-zero field at each point of the surface; the inward and outward contributions merely cancel in the integral. Zero net flux does not mean zero field.

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