# Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

## Homework 6 - Due October 15, 2015 in class

1) In the reflection problem about a conducting sphere and a point charge (Example 3.2 in Griffiths and discussion in class) we assumed that the sphere is grounded (i.e. V=0). But with addition of a second image charge the same basic model will handle the case of a sphere at any potential Vo (relative, of course, to infinity). Think about where you should put that charge to keep the surface of the sphere equipotential.

Determine the force between the point charge and ungroudned and uncharged sphere. Take radius of sphere to be R and the distance between the point charge and the center of the sphere to be d.

2) In a grounded block of conductor there is a spherical hollow (see the sketch).

The center of the hollow is at point O, and the radius of the sphere (i.e. distance between points O and A is R. At a distance d from point O placed a charge q. Find the charge density of induced charges at point A.

3) Two infinite conducting plates are perpendicular to each other. A charge q is placed distance a from their intersection, along the bisector.

Find the force F acting on the charge.