A solid nonconducting sphere of radius R has a charge Q uniformly distributed throughout its volume. A Gaussian surface of radius r with r < R is used to calculate the magnitude of the electric field E at a distance r from the
center of the sphere. Which of the following equations results
from a correct application of Gauss’s law for this situation? And Why?

1. E (4 p r^2) = (Q r^3)/( epsilon sub0 * R3)
2. E(4pr^2)= (Q 3r^3)/ (epsilon sub0 * 4 p R)
3. E (4 p r^2) = (Q) / (epsilon sub0)

or

Explanation:

We know that Gauss's law states that the Flux enclosed by a Gaussian surface is given by

Here , E is electric field and S is surface are and q is charge enclosed by the surface and e is electrical permeability of the medium.

Here the Gaussian is of radius r<R so area of surface is

Also, charge enclosed by the surface is

therefore,

Here Q is total charge,

Insert values in Gauss's law

Rearrange them

on further solving

This is the required form.

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find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle