# Why is there no induced charge outside of the conductor?

• I
• annamal
In summary, when the amount of positive and negative charges inside a conductor is not equal, there will be induced charges on the outermost surface of the conductor.

#### annamal

If we put a positive charge outside of a conductor, there is an induced charge, but if we put a positive and negative charge inside a conductor, there is no induced charge?

Ibix said:
I don't get it. A faraday cage creates charge on the outside of the conductor and blocks charge going in...

vanhees71
I'm not sure, I understand the question. No matter, where you put the charge (inside or outside) the conduction electrons in the conductor rearrange such that, after a (usually pretty short) relaxation time, you are in a static state such that the boundary conditions along the surface are fulfilled.

If you put the charge outside, this arrangement is such that in the interior the electrostatic field vanishes ("Faraday-cage" effect). There's of course an electric field everywhere, when you put the charge inside.

It's very illuminating to completely solve the problem for a conducting spherical shell, which you can solve analytically using the method of image charges. For the sphere it's not too difficult, because one image charge is sufficient. You should find this problem in any good textbook on electrodynamics. I'm pretty sure, it's in Jackson.

annamal said:
I don't get it. A faraday cage creates charge on the outside of the conductor and blocks charge going in...
...or charges on the inside to block electric fields going out. The diagram, I think, shows an ellipsoidal body with two spherical hollows, each containing a charge. There is an induced charge on the surface of the hollows (the inside surface of the conductor) but nothing on the outside surface because there's no net charge inside and the electron distribution on the inside surface cancels out the dipole field.

Ibix said:
...or charges on the inside to block electric fields going out. The diagram, I think, shows an ellipsoidal body with two spherical hollows, each containing a charge. There is an induced charge on the surface of the hollows (the inside surface of the conductor) but nothing on the outside surface because there's no net charge inside and the electron distribution on the inside surface cancels out the dipole field.
If we had one cavity of charge, that would induce a charge on the surface.

annamal said:
If we put a positive charge outside of a conductor, there is an induced charge, but if we put a positive and negative charge inside a conductor, there is no induced charge?
The charge does not appear inside the conductor, so the charge cannot simply be placed inside the conductor, so a more accurate expression is as shown in the figure below. There must be an insulating layer, the charge will accumulate at the interface of the conductor and the insulating layer, so here is the electric field in the insulating layer.

alan123hk said:
The charge does not appear inside the conductor, so the charge cannot simply be placed inside the conductor, so a more accurate expression is as shown in the figure below. There must be an insulating layer, the charge will accumulate at the interface of the conductor and the insulating layer, so here is the electric field in the insulating layer.

You drew induced charges on the surface of the conductor. There are no induced charges.

annamal said:
You drew induced charges on the surface of the conductor. There are no induced charges.

I believe you mean that there will be no induced charges on the outermost surface of the conductor, but why are you so confident or so sure?

alan123hk said:
I believe you mean that there will be no induced charges on the outermost surface of the conductor, but why are you so confident or so sure?
The beginning of the thread I posted a picture from my textbook and it says no induced charge outside.

annamal said:
The beginning of the thread I posted a picture from my textbook and it says no induced charge outside.

Got it, maybe I'm wrong. But until I see theoretical evidence that convinces me, I can only continue to believe the following.

When the positive and negative charges placed inside the conductor are not equal, there must be induced charges on the outermost surface.

When the amount of positive and negative charges placed inside the conductor is equal, depending on the shape of the conductor and the position of the charge distribution inside the conductor, the outermost surface may have no induced charge, or there may be induced charge.

At present I dare not rule out the second possibility.