Gauss's Law

Gauss's Law states that the total electric flux through any closed surface is equal to the net charge enclosed divided by the permittivity of free space: (\Phi_E = \frac{Q_{enc}}{\varepsilon_0}). This is one of the most fundamental results in electrostatics and holds regardless of the size or shape of the Gaussian surface. The flux depends only on the net charge enclosed, not on the shape, size, or position of the surface. Since both surfaces (radius 15 cm and radius 30 cm) enclose the same point charge (Q), the total flux through each is (\Phi = Q/\varepsilon_0). Option 'It doubles' is incorrect because increasing radius does not change the enclosed charge. Option 'It halves' is incorrect because the flux is independent of surface size for the same enclosed charge. Option 'It increases four times' is incorrect because this would be the change in surface area, but flux is not proportional to area alone. This is a direct JEE Main application of Gauss's Law and is commonly tested as a conceptual question. Plausibility check: all field lines emanating from the charge must pass through any surface surrounding it, confirming constant flux.