# Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

## Homework 5 - Due October 8, 2015 in class

1) Calculate the potential inside a parallel plate capacitor with plate separation *d*,
provided that:
one of the plates is grounded
the other is maintained at potential *Vo*
the space between the plates has uniform charge density ρ

2) Two spherical cavities, of radii *a* and *b*, are hollowed out from the interior of
a (neutral) conducting sphere of radius *R* as shown below.

At the center of the cavities, known charges *Qa* and *Qb* are placed.

a) Find the surface charge densities σa, σb and σR

b) What is the field outside the conductor?

c) What is the field within each cavity?

d) What is the force acting on *Qa*?

3) Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radii *a* and *b* (see figure below)