# Physical example of line charge

Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism.

My question: does an (exact or approximate) example of "infinite/finite line of charge" exist in the physical world?

While we find application of sheet of charge (though finite, not infinite) in case of capacitors, and i can imagine the physical presence of point charge and spherical charge, etc, but a line of charge with uniformly distributed charge density, which basically means a thin conductor with charge Q per unit length - can we have such a thing?

As i understand:

1. If we connect a battery to a straight wire, with circuit closed, we get a current, but still, any section of the wire is charge-less. So, not an example of line charge.

2. If we connect a battery to a wire, with circuit not closed, the charges inside the conductor will move within so as to cancel the applied electric field. So again the conductor won't have uniform charge, so not an example of line charge.

3. If we connect ac voltage to a wire, we get sinusoidal charge variation along the wire, so, again not an example.

Can anyone please give a realistic example, which can come close to a line of uniform charge.

## 2 Answers

Line charges are used in wire chambers, an apparatus used for high energy physics experiments.

There are lots of ways to make a line of charge. The easiest ones involve putting a charge on a wire. For example, make a large, thin metal ring of conducting material. Place the ring on an insulated stand. Place a positive or negative charge on the ring (perhaps with a Holtz machine). Look at the ring very close up, so that the wire appears close to straight, yet not so close that the wire's thickness starts to matter. You now have an approximate line of charge.

• thanks a lot. I have to know about wire chamber and Holtz machine.What is the significance of 'ring' there? What that set up does basically is: place some charge on an isolated piece of wire and it becomes uniformly distributed along its length. So any shape, not just ring, should be okay. Is it? – RKG Mar 12 at 12:48
• The ring is necessary here to get a uniform distribution. If you just place a charge on a straight length of wire then there'll be more charge on the ends of the wire so the charge won't be uniformly distributed. – lsusr Mar 12 at 20:02

The magnetic field due to a current in a wire can be derived by considered it to be the resultant of Coulombic fields arising from (a) a line of positive ion-cores in the wire and (b) a moving line of electrons. Bearing in mind length contraction, it can be shown (for example Resnick: Intro to Special Relativity) that the charge densities for (a) and (b) cannot be equal and opposite in any but one inertial frame of reference, hence 'a residual field' outside the wire, having (it turns out) the characteristics of a magnetic field.

I suspect that this case technically meets your requirement, but that you were looking for a straightforward case of a line of charge. At least my example – a current-carrying wire – is pretty everyday, though the analysis may not be!

• very interesting view of this problem. That's a good enough example, i think. – RKG Mar 12 at 12:54