Why are mirror charges created?

[CraigH]

When a charge is placed next to an uncharged conductor, a mirrored image of that charge is created on the other side of the uncharged conductor. The mirrored image charge will have an equal and opposite magnitude to the original charge.

For example, if there was a 1C point charge 1m away from a thin metal sheet, it will appear as if there is a -1C point charge on the other side of this metal sheet.

The electric field lines in the x direction would look like this:

+o--------->|--------->o-

Why does this happen? All I know so far is that when a conductor is placed inside an electric field, the charges inside it are re-arranged. This seems intuitive, as an electric field is just a vector field that denotes what force a positive 1 coulomb charge would feel a particular point in space, so the charges inside the conductor will have a force on them, and will move until they are in a position where there there is no net force on them. This will be when the electric fields inside the conductor cancel out.

In my example diagram the positive charge will cause the electrons inside the conductor to move towards this charge, they will continue moving until the fields cancel out. I can see that this would also be true if an opposite charge was placed at the other side of the conductor. The electrons inside wouldn't be able to tell the difference.

But just because this is true does not mean that the fields on the right side of the conductor will act as if there is a mirror charge there.

I don't understand why a mirror charge is created. Will someone please explain?

Thanks.

Also, mini extra question:
How does this apply to antenna's? It's something to do with dipoles but I don't properly understand what is happening. If you could give an example of mirror charges being created in the context of an antenna It will be greatly appreciated!

 

[mfb]

Why does this happen?

It is the only solution with zero electric field everywhere inside and along the metal sheet. It is easy to see that it is a solution, and mathematics guarantees you that it is the only solution.

How does this apply to antenna's?

I don't see a relation to antennas.

 

[CraigH]

Okay thanks, I think I study the maths in more detail next year. After that i'll probably be able to believe that it is the only solution :)

I don't see a relation to antennas.

A dipole antenna radiates an EM field because of the accelerating and decelerating charges inside of it. The electric field will be oscillating as it can not change at the same place everywhere at the same time (the wave front travels at c), and the magnetic field oscillates because a moving charge causes a magnetic field, and the charge is accelerating and decelerating in simple harmonic motion. This means at the point where acceleration is maximum and velocity is zero, there will be no magnetic field, and at the point where acceleration is minimum and velocity is maximum there will be maximum magnetic field.

What mirrored charges have to do with this:

In a dipole antenna the oscillating charges inside the antenna are reflected in the ground plane. This creates the dipole. The combination of the oscillating dipole charge, and the oscillating charge's in the antenna creates An EM wave.
http://upload.wikimedia.org/wikipedia/commons/a/aa/VFPt_dipole_animation_electric.gif
The fact that antennas work prove that these dipoles exist. Understanding them is important for antenna theory, it is the reason I asked this question. Just because a dipole is a solution to what caused the re distribution of charge inside the conductor shouldn't mean that it is actually there. Should it?

 

[mfb]

I still don't see a relation between moving charges in antennas and mirror charges in electrostatic setups.

Just because a dipole is a solution to what caused the re distribution of charge inside the conductor

There is no (interesting) dipole in the static setup. The mirror charge is imaginary.

 

[sophiecentaur]

Any induced charge on an object will not actually produce any net imbalance of charge. Any excess of - charges on one side of it must result in an excess of + charges on the other side, to compensate.

 

[pumila]

The mirror charge does not exist. It is used as an artefact that allows the field lines between the ground plane and the real charge to be calculated more readily. Essentially, the field lines between the real charge and the real ground plane are identical to the field lines between the charge and the mirror charge in that region, so one simply calculates the field lines between the real charge and the mirror charge (ignoring the real ground plane) to find the strength and shape of the field lines between the real charge and the real ground plane.