## The Best asnwer for An insulating sphere of radius a, centered at the origin, has a uniform volume charge density p.?

Throughout this E, r, h, and d will denote vectors.

First find the electric field a a sphere without the cavity:

q = ρV = ρ(4/3*πr^3)

E = kq/r^2 = kρ(4/3πr^3)/r^2 = 4kρπr/3 = ρr/(3ε_0)

A cavity has no charge, which is the same as having two equal and opposite charges. Find the electric field of such an opposite sphere:

E_opp = -ρd/(3ε_0)

This is the same as above, just using d to denote the distance from the center of the opposite sphere. Because the sphere is centered at h in the sphere, d = r - h:

E_opp = -ρ(r - h)/(3ε_0)

E_cav = E + E_opp = ρr/(3ε_0) - ρ(r - h)/(3ε_0) = ρh/(3ε_0)

Lorem ipsum dolor sit amet, consectetur adipiscing elit,
sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam,
quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor
in reprehenderit in voluptate velit esse cillum dolore eu fugiat.

SHOW ANSWER