J(r) =

J(r) =

MCS 279 Vector and Complex Analysis Summer 2001 Selected Recitation Problems in Week 6 Gauss’ Law and Ampere’s Law 1. Consider the spherical charge di...

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MCS 279 Vector and Complex Analysis Summer 2001 Selected Recitation Problems in Week 6 Gauss’ Law and Ampere’s Law 1. Consider the spherical charge distribution defined below. Find the electric field everywhere. ,r  0

q

>

,0  r  a

0 Ÿ> 0 sin r /r

2

,a t r t b

2. Consider the cylindrical charge distribution defined below. Find the electric field everywhere.

>

>l

,r  0

0

,0  r  a

Ÿ> 0 e "r  /r

,a t r  b

3. Consider a uniform surface charge density, > s , extending to infinity in the horizontal plane Ÿx " y plane). Use Gauss’ Law to find the electric field above and below this plane. 4. Consider an infinitely long coaxial cable that has the following current density distribution. Find the magnetic field everywhere. JŸr  

J 0 sinŸr=/2a  r

k, 0 t r t a

0, r  a