10 An insulating sphere with radius r 15 cm has some total charge Q and some vol

Question

10 An insulating sphere with radius r 15 cm has some total charge Q and some volume charge density A student imagines a Gaussian surface which is a sphere with radius 30 cm. Which of the following changes would result in an increase of the flux through this Gaussian surface? a) Reduce the radius of the insulating sphere to 5 cm while keeping Q constant b) Reduce the radius of the insulating sphere to S cm while keeping p constant c) Increase the radius of the insulating sphere to 25 cm while keeping Q constant d) Increase the radius of the insulating sphere to 25 cm while keeping constant

Explanation / Answer

Answer is : d)increase in radius of the insulating sphere to 25 cm while keeping rho constant.

Explanation:

Flux through a Gaussian surface is given by:

Phi = Q/epsilon

So, flux is only dependent on the total charge inside the surface.So, options (a) and (c) are incorrect as they don't increase the charge Q

Now, as the radius is decreased to 5cm (for case (a)), the charge inside the Gaussian surface decreases. So, this option is also incorrect.

Now, option (d) is correct as the total charge increases as the radius increases.

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