Gauss's Law: Finding Electric Field of Line of Charge

[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?

 

[david456103]

anyone?

 

[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.

 

[SammyS]

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?

anyone?

Please be patient. There are rules on this forum regarding the "bumping" of your thread.

Now, for your question regarding the electric field due to a line of uniform charge at a height x from the line of charge, "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?"

We can apply Gauss's law no matter what. However, if you want to apply Gauss's law to calculate the electric field at some particular location, there have to be some very stringent requirements that are met. This is because of the very nature of the law.

Gauss's law relates the amount of electric flux exiting any closed surface to the net electric charge within that closed surface. So, it can always be used to calculate flux through a closed surface, if you know the net electric charge within that surface. It can also be used in the other direction, by using the flux through the surface to calculate the total charge inside.

But since this is the homework section, maybe we should let you tell us why we can only apply Gauss's law to calculate the electric field if the line is of infinite length or if x is small compared to the length of the line of charge?