# Field lines within a conductor

I am trying to comprehend the field lines within a conductor and why the fields lines and charge within a conductor is zero.

Assume a charged conductor as shown in Attachment 1.png. Here there is a charge and the charges exert a force on each other. I can imagine how these charges would force each other away and so end up on the outside of the conductor. For example, assuming you had three charges, they’d create a ‘triangle’ on the diameter of the circle…

So, at some point the charge on the conductor would appear something like Attachment 2.png, and at the edge on a microsopic level I imagine would appear something like Attachment 3.png. But there is still a force acting within the conductor from the charges on the outside.

So

1. Why should there be no field lines within the conductor?
2. At some point, the charge on the outside will be so great that the charges can’t help but separate within the conductor as per Attachment 4.png?

Thank you!

An electric charge has both a magnetic field and an electric field. They are oriented 90 degrees from each other. Which one are you concerned with?

Paul

Field lines are the transverse to gradient lines - like on a weather map.

There are (apart from due to its resistance) no gradients inside a conductor as all points are at the same potential - so all field lines will exit perpendicularly.

This is an electrostatics question, so no magnetic field.

You need to think in terms of the E-field, not the individual charges interacting.

If there was any E-field inside the conductor, the free charges in it will move/drift. Thus you are not
in an equilibrium situation (so its electrodynamics, not electrostatics). Once equilibrium is established
you know no field exists inside any conductor (as no charges are moving) thus the charges are fully
balanced in the interior, and unbalanced charge can only exist at the surface, and you can further
deduce the E-field comes out of the surface at right angles to it (otherwise surface charges would move along
the surface).

All of electrostatics assumes equilibrium states... The above is a powerful argument, it doesn't care
how things happen, only that if equilibrium is established, the fields are as described. The argument
doesn't even imply that equilibrium is possible!

Net charge (density) inside a conductor is zero, of course there is charge, but its fully balanced.

Once currents flow the above arguments completely vanish of course. It gets more complex with DC
currents, and more complex again with AC currents (changing magnetic fields become important).