# Electric field in a cavity in a spherical charge density

1. May 12, 2017

### Ruby_338

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
E =
q2/4πεr2
Where ε is permittivity of medium.
Electric flux,Φ= q/ε where q is net charge inside gaussian surface.
3. The attempt at a solution
I don't even know where to begin

2. May 12, 2017

### 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.

3. May 13, 2017

### Ruby_338

Thanks. I'll try that