HOW TO CALCULATE ELECTRIC FIELD OF SOLID SPHERE

We have spherical symmetry, and that immediately suggests we can use a sphere as our Gaussian surface.  So draw the imaginary Gaussian sphere with radius r inside the actual charged sphere, and write down Gauss’ law.

Now we know E is going to be emerging perpindicularly to our Gaussian surface, thus the dot product is just E da.  And E is constant over the surface, so we just have

But the integral is now just the total area of the sphere: 4 pi r^2.  Thus,

And the charge enclosed is the point charge Q plus however much of the solid sphere’s charge we enclose is.  And that latter quantity is just the volume of the Gaussian sphere times the charge density ?.  Substituting,

Divide to solve for E and we’re done!

Inside a sphere:

take a gaussian surface of radius 'r'.

E.4∏r^2=1/e0 *Qr³/R³   (total flux=enclosed charge by abbsianal not)

you can solve this eqn to find E.

Similarly for a point outside the sphere, take a gaussian sphere of radius 'r'(>R) and follow the same steps.