# Infinite Number of Image Charges?

• bob012345
In summary, when considering two opposing mirrors, if they are perfectly parallel there is only one image in each, but if they are slightly angled, there can be an infinite number of reflections. Similarly, for grounded conducting planes with a charge in between them, if they are perfectly parallel there are two image charges, but if they are misaligned, there can be a finite number of images depending on the angle. This phenomenon is known as the method of images and it also exists in magnetostatics. In both cases, there can be images of images ad infinitum. For two perfectly parallel grounded, conducting planes with a charge in between, the number of image charges is infinite and any forces on the real charge cancel out. If the planes are
bob012345
Gold Member
Consider two opposing mirrors. If they are exactly parallel planes I think there is only a single image in each but if they are slightly angled there appears an "infinite" number of reflections. Similarly, suppose we have grounded conducting planes instead of mirrors with a charge in between them. I think if they are perfectly parallel there are exactly two image charges. But if they are slightly misaligned will there be an multiple series of image charges appearing to go to infinity? If so, will the actual number of images depend on the angle? Thanks.

p.s. Now I'm not sure if there are or aren't an infinite number of images when mirrors are exactly parallel. I can't see them since my own image blocks them.

p.s.2 On further reflection...Of course there must be.

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There are a seemingly infinite number of images whether or not the mirrors are parallel.
If you are looking straight into one of those mirrors, your first image will completely hide the others.
But stick your hand out to the side (with your arm bent - as if you were waving to yourself) and try counting how many images of your hand there are.

vanhees71 and bob012345
bob012345 said:
Like a seeming infinite number of images occur in opposing mirrors, does a similar situation occur with opposing infinite grounded, conducting planes with a charge in between them?

Yes. It's called the method of images. (A far less known but similar method of images exists in magnetostatics.)

In both of your cases one gets images of images ad infinitum.

vanhees71 and bob012345
Thanks. So for two perfectly parallel grounded, conducting planes with a charge in between, the number of image charges is infinite and any forces on the real charge cancel out. If the planes are angled the number of images is finite and should be dependent on the angle and there would be a net force on the charge acting towards the intersection of the two planes just as there is a force when a single charge is located near a single plane.

## 1. What is an infinite number of image charges?

An infinite number of image charges is a theoretical concept in electrostatics where an infinite number of point charges are placed in a specific pattern to mimic the electric field of a given charge distribution. This technique is used to simplify complex charge distributions and solve problems in electrostatics.

## 2. How is an infinite number of image charges created?

An infinite number of image charges are created by placing point charges at specific distances and orientations from a given charge distribution. The number of image charges required depends on the geometry of the charge distribution. As the number of image charges increases, the accuracy of the electric field approximation also increases.

## 3. What are the applications of an infinite number of image charges?

An infinite number of image charges are commonly used in electrostatics to solve problems involving conductors, dielectrics, and other charge distributions. They are also used in the design and analysis of electrical systems and devices, such as capacitors, antennas, and electric circuits.

## 4. How accurate is the electric field approximation using an infinite number of image charges?

The accuracy of the electric field approximation using an infinite number of image charges depends on the number of image charges used and the complexity of the charge distribution. In general, the approximation becomes more accurate as the number of image charges increases.

## 5. Are there any limitations to using an infinite number of image charges?

While an infinite number of image charges can provide a good approximation of the electric field, it is not a perfect solution. The technique assumes that the charge distribution is static and does not take into account the effects of time-varying fields or moving charges. It is also limited to problems involving electrostatics and cannot be applied to other areas of physics.

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