# 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.