Electric field in a cavity in a spherical charge density

[Ruby_338]

Homework Statement

A uniform spherical charge density of radius R is centred at origin O. A spherical cavity of radius r and centre P is made. OP = D = R-r. If the electric field inside the cavity at position r is E(r), the correct statement is:
1)E is uniform, its magnitude is independent of r but its direction depends on r
2)E is uniform, its magnitude depends on r and direction depends on r
3)E is uniform, its magnitude is independent of D but direction depends on r
4)E is uniform and both it's magnitude and direction depend on D.

Homework Equations

E = [/B]q²/4πεr²
Where ε is permittivity of medium.
Electric flux,Φ= q/ε where q is net charge inside gaussian surface.

The Attempt at a Solution

I don't even know where to begin

 

[kuruman]

Begin by finding the electric field inside a sphere of uniform volume charge density. Then consider superposition. You get zero charge by adding a positive spherical distribution and a negative spherical distribution so if you add a spherical distribution centered at P of opposite charge, you get a cavity.

 

[Ruby_338]

Thanks. I'll try that