- #1

prosteve037

- 110

- 3

- Homework Statement
- What should the charge density ρ(x, y, z) in a sphere be so that there's a constant radial (it's always parallel to the radius) electric field E_0 at every point inside the sphere?

- Relevant Equations
- Maxwell's equations, specifically Gauss' law for electric fields, maybe some boundary conditions?

I'm having trouble understanding how a charge distribution in a sphere can make this happen.

My instinct is that the fact that it's radially directed is a big hint of something, but I don't know what that hint might be alluding to. If the net E-field is constant inside the sphere and is always directed radially outward, as one moves in any direction from the center, wouldn't the charges have to move/redistribute (as in the case for a conductor) in order for the E-field to remain the same value?

I'm not sure if any of the other Maxwell's equations gives any hints, but I don't think so.

My instinct is that the fact that it's radially directed is a big hint of something, but I don't know what that hint might be alluding to. If the net E-field is constant inside the sphere and is always directed radially outward, as one moves in any direction from the center, wouldn't the charges have to move/redistribute (as in the case for a conductor) in order for the E-field to remain the same value?

I'm not sure if any of the other Maxwell's equations gives any hints, but I don't think so.