Question

A non-conducting sphere of radius R a has a charge uniformly distributed in it with a charge density of p. Find the electric field at a point outside the sphere a distance r from the center.

Answer 1

Since the amount of charge distributed across the sphere is unknown, first consider a small area of volume upon the sphere. let this small volume be "dv". Consider the charge spread over this small volume as dQ.
Now let us assume that electric field due to this small volume dv at a point be dE.
Firstly calculating dE at a point due to dQ. i'm sorry if i confused you. here is how it is done.
Electric field dE at a point P due to dQ is given by
dE=dQ/(4piϵR^2 )=p*dv/(4piϵR^2)
ϵ is permitivity of free space. its value is 8.854*10^-12
After you get this value if we do volume integration over the sphere we get total electric field due to entire sphere.
\[\int\limits_{vol}^{}\]dQ/(4piϵR^2 )