# Homework Help: Sphere above thin conducting sheet

1. Mar 2, 2010

### irrek

A sphere of mass m = 0.45 kg is suspended 0.20 m above a thin sheet of charge with an area of 0.65 m2 and uniform surface charge density σ. The sphere has a uniform charge density of 4 nC/m3 and a radius of 3.2x10-3 m. You may ignore adverse field effects from the edges of the sheet of charge, meaning that you may expect a uniform electric field from the conducting sheet.

1. Find σ, the surface charge density of the thin conducting sheet.
a. Find the total charge of the thin conducting sheet.

Keeping the same configuration as above, the thin conducting sheet is now replaced by a dipole made of two identical point charges fixed to the x-axis a distance d = 0.55 m apart. The position and orientation of the sphere does not change.

2.. What must the sign of each charge be to support the sphere?
3. Calculate the magnitude of each point charge.
4. Find the angle between the vector forces from each charge in the dipole
5. Report the straight line distance between each point charge and the sphere of charge.

A position vector P has a magnitude of 1.25 m and makes an angle φ = π/3 rad with the +x-axis.

6. Given the configuration of the dipole and charged sphere above, what is the electric field at point P?
7. If the magnitude of P were tripled what would happen to the magnitude of the electric field?

E = σ/(2ε0)
mg = qE

All I've been able to figure out is the very first question.
m = 0.45 kg, ρ = 4 nC/m3, r = 3.2*10-3 m,
charge on the ball q = ρ*(4πr3/3)
E = σ/(2ε0)
mg = qE
mg = ρ*(4πr3/3) * σ/(2ε0)
σ = 3ε0mg/(2πρr3) = 1.42*105 C/m2

After that, I'm completely lost
!