# Gauss's Law help!

1. Oct 8, 2012

### david456103

Suppose we want to find the electric field of a line of uniform charge at a height x from the line. Why can we only apply Gauss's law if the line is of infinite length or if x is small compared to the length of the line of charge?

2. Oct 8, 2012

anyone?

3. Oct 8, 2012

### rbj

consider a finite cylinder with the cylinder axis coincident with the line of charge and with radius x. then make an argument of symmetry about E-field lines extending in any direction other than straight out from the line of charge.

then apply Gauss's law. the amount of charge inside of the surface is proportional to the length. the area of the outside of the cylinder is proportional to the length and to x. the surface of the cylinder on the two ends (disks with radius x) have no E-fields lines crossing them due to the symmetry argument.

do a little bookkeeping and you'll have an answer for the field strength.

4. Oct 8, 2012

### SammyS

Staff Emeritus