Electrostatics Of Conductors

Question

My textbook says that no excess charge can reside inside the conductor because electric field inside a conductor is 0. But say i introduce a positive charge inside a conductor, it generates its own electric field and interacts with the free electrons and the nucleus inside the conductor which i feel is the only interactions that the charge faces.

Then my question is how based on these interactions the charge move and resides at surface of conductor?

So basically how does an excess of charge move and reside at surface of conductor on its own?

Answer 1

A conductor has mobile/free charge carriers and in the case of a metal these charge carriers are electrons which are not bound to any particular nucleus.

Copper in the gaseous phase has 29 electrons orbiting each nucleus and the nucleus contains 29 protons.
The copper atoms are electrically neutral.

When in the liquid or solid phase on average one of the electrons per atom ceases to orbit a particular copper nucleus and is able to move freely within the whole of the metal in a way which is similar to the random movement of atoms in a gas. Left behind are positive copper ions whose movement in a liquid is restricted and in a solid is limited to vibration about fixed locations within the solid. The reason for the atoms doing this is that it is energetically favourable to do so and the result is called a metallic bond.

When discussing electrostatics there cannot be an electric field inside a conductor because if there was an electric field then the mobile charge carrier under the influence of that electric field would move and redistribute themselves to produce a situation such that there was no electric field inside the conductor.

When a conductor is uncharged it means in an ideal situation that total number of positive charges (protons) is equal to the total number of negative charges (electrons) and the net electric field inside the conductor is zero.

Now suppose that some mobile electrons are removed from a void inside an initially uncharged conductor.
This is equivalent to adding positive charges to the void as stated in your question. The removal of free electrons results in an electric field being produced inside the conductor because now there is a surplus of positive copper ions around the void.
Those copper ions would produce a net electric field inside the conductor which would be felt by all the other copper ions as well as the mobile electrons within the conductor.
Because they can undergo significant movement the mobile electrons would move towards the surplus of copper ions around the void and continue to do so until the net electric field inside the conductor became zero.
In this state the conductor would have a net deficit of mobile electrons on the surface and this can be interpreted an positive charges residing on the surface of the conductor which are the positive ions with not quite so many mobile electrons moving randomly around them.

Answer 2

When a conductor is placed in any external electric field, generated by any source, then the net charge inside the volume of the conductor is zero. Why? Consider the situation when the electric field is "switched on". Then, as a conductor allows free movement of electrons, and thus _charge_ inside its volume, so the charges start moving inside the conductor.

Now, when will the charges stop moving? When another force stops them from moving, by opposing and cancelling out the force due to the electric field. Inside the volume of the conductor, in the ideal case, there will be no other force on the charge (in the form of presence, or lack of electron). But, when a charge reaches the boundary of a conductor, something changes. Considering a negative charge, or an electron, deep inside the volume of the conductor, the force due to the positive nuclei on the charge would cancel each other, but near the surface, all the postive nuclei would pull in the same direction. For a postive charge, this would mean a lack of electrons, which moves by drawing electrons from nearby regions. This cannot happen at the boundary of the conductor. All this would, simply put, prevent a charge from escaping the volume of the conductor. So, we see that ancharge in a conductor will keep moving till it reaches the surface of the conductor, where it stops.

Now, when the charges have reached the surface, why don't they move around the surface? Well, they do move around, till the field generated due to the other charges (accumulated on the surface) prevents our charge from moving even along the surface! When both kinds of motion (towards the surface and along the surface) stop, then we get the final charge distribution on a conductor. All this happens within a very short time of around few milliseconds.

Finally, if you take the specific example of placing a positive charge somewhere inside the conductor, the same reasoning applies, that is:

• the electrons from surrounding regions are attracted to the positive charge,

• the electrons from further regions are attracted to the newly created positive region, and so on,

• till the positive charge reaches the surface and there are no more electrons to attract from outside the conductor, finally making the postive charge reside on the conductor's surface.