# Homework Help: Point Charge around a sphere

1. Oct 14, 2007

### Bloodplasma

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

A point Charge Q is placed a distance R from the center of a conducting sphere of radius a, with R>a, i.e. the point charge is outside the sphere. The sphere is grounded- connected to a distant, unlimited source/sink of charge at zero potential. (Neither the distant "ground" nor the connection directly affects the electric field in the vicinity of the charge and sphere.) As a result, the sphere acquires a charge opposite in charge to Q, and the point charge experiences an attractive force toward the sphere.

Remarkably, the electric field outside the sphere is the same as would be produced by the given point charge Q plus a mirror image point charge q, of such value and location as to make the set of point corresponding to the surface of the sphere an equipotential of potential zero. That is, the fictional "image charge" gives the same field contribution outside the sphere as the actual surface charge on the sphere. Calculate the value and location of charge q. HINT: By symmetry, charge q must lie somewhere on the axis which passes through the center of the sphere and the location of charge Q.

2. Relevant equations

3. The attempt at a solution

I am assuming its a solid sphere of uniform density, other then that i am not sure how to go about solving this.

2. Oct 14, 2007

### Phred101.2

Mate, it's about Gauss' Law. Haven't you got any books?

3. Oct 16, 2007

### clem

It's not Gauss, but the method of images, which should be described in your textbook.