Why is the electric field zero at a grounded conductor plate despite induced charge?

[Hootenanny]

Let's look at the following setup: A point charge Q is placed at the center of a spherical, hollow conductor with inner radius a and outer radius b. Since the conductor has no net charge, a charge of -Q will spread uniformly over the inner radius and a charge Q on the outer radius.

These are the free charges inside (at least the electrons), and it makes good sense that they divide up like that since there are no free net charges inside the conductor. But my questions is - will these charges lie outside on the surface of the conductor?

Yes, electrons will move away from the outer surface and towards the inner surface, leaving a deficit of negative charge on the outer surface and an excess of negative charge on the inner surface. As you say, this charge will be uniformally disributed over the inner and outer surfaces of the sphere, but there will still be no net charge insider the sphere.

Now let's take another setup: This is like the former one, but now a charge Q' is placed on the surface of the conductor. Then a charge -Q must still reside at the inner radius and a charge of Q'+Q must reside on the outer radius. Sinse there are no net free charges in the conductor, all these charges lie on the surface of it as well?

Correct again.

 

[Niles]

Okay, so how does this initially neutral sphere acquire a net negative charge? Where does this negative charge come from?

Hi Hootenanny

I'm still thinking about this. Say we have a conducting sphere in an electric field, and all the electrons pile up on the right side and there's a deficit of negative charges on the left side. We place a grounded metal-stick on the right side.

Now, why is it that the electrons cannot go into the ground? I know there's no net charge inside or outside the conductor, but what is the argument that tells me that the electrons cannot go to the ground even if the electric field is very strong?

 

[Hootenanny]

Hi Hootenanny

I'm still thinking about this. Say we have a conducting sphere in an electric field, and all the electrons pile up on the right side and there's a deficit of negative charges on the left side. We place a grounded metal-stick on the right side.

Now, why is it that the electrons cannot go into the ground? I know there's no net charge inside or outside the conductor, but what is the argument that tells me that the electrons cannot go to the ground even if the electric field is very strong?

What makes you think that they won't go to ground?

 

[pzlded]

If indeed a point charge causes point charge displacement in a grounded plate, energy must be expended displacing the charges. Voltage's energy is stored in capacitors, therefore the grounded plate and point charge form a capacitor.

The solitary point charge has a field that influences every point charge in the plate. What is weird is that the number of charges on each plate of a capacitor is equal. Therefore a single point charge in the plate is displaced; all other charges are not displaced.

 

[Niles]

What makes you think that they won't go to ground?

I don't know why, actually.. it struck me after I had posted. It's only if we place the grounded metal-stick on the side with the deficit of negative charges that additional negative charges are drawn from ground, since the atoms are fixed in the lattice.

 

[Hootenanny]

I don't know why, actually.. it struck me after I had posted. It's only if we place the grounded metal-stick on the side with the deficit of negative charges that additional negative charges are drawn from ground, since the atoms are fixed in the lattice.

Correct! For example, one can charge a conducting sphere using this method. If one places a conducting sphere with a grounding cable in an external electric field then the electrons will move to one side of the sphere and down the grounding cable (provided that the grounding cable is on the correct side) such that the area immediately around the grounding cable is electrically neutral. However, the side opposite the grounding cable with have a net positive charge. Now if the grounding cable is detached and the external electric field removed, then the sphere will have a deficit of electrons and hence will have gained a net positive charge.

 

[pzlded]

Drawing an electron from a grounded metal-stick is current. Current must obey Kirchoff's law (point charges in = point charges out).

Does ground really supply an electron to the plate? A capacitor has the same energy w/ or w/o a grounded plate. Is there an energy advantage to drawing an electron from ground?