# Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

## Homework 9 - Due November 12, 2015 in class

1) A coaxial cable consists of a copper wire of radius *a* inside a copper tube
of inner radius *c*. The inside of the tube is covered by a layer of linear dielectric,
with dielectric constant *ε*_{r}, so that the inner radius of the dielectric is
*b*.

Find the capacitance per unit length of that cable.

2) An uncharged conducting sphere of radius *a* is insulated with a layer of linear dielectric,
with dielectric constant *ε*_{r}, so that the outer radius of the dielectric is
*b*. This object is now placed in an otherwise uniform electric field *E*_{0}.
Find the electric field inside the dielectric.

3) In the previous problem set up, calculate the surface charge density on the metal sphere, and bound charge
density on the inner surface of the dielectric. Compare with the case we considered earlier in the class -
Griffiths example 3.8 (uncharged conducting sphere in elecric field).

4) Two long coaxial cyllindrical metal tubes of radii *a* and *b*, stand vertically in a tank of oil
of mass density ρ and dielectric constant *ε*_{r}. The inner tube is maintained at potential
*V*_{0}, while the outer is grounded. To what height would the oil rise into the space between the tubes?