How does the method of image charges work between two conducting surfaces?

In summary, the method of image charges involves creating an imaginary charge above a single conducting surface. However, if the charge is between two conducting surfaces, the bottom plate and imaginary charge will be reflected across the top plate above the real charge. This can be done in steps, resulting in an infinite chain of charges.
  • #1
dimensionless
462
1
I'm reading about the method of image charges at

http://en.wikipedia.org/wiki/Method_of_image_charges

The page describes a charge located above a single conducting surface. What happens if the charge is between two conducting surfaces? Does the bottom plate, along with the imaginary charge get reflected across the plate above the real charge? I've typed a simple diagram below.


(+) imaginary charge

------------ imaginary plate

(-) imaginary charge

========== real plate

(+) real charge

========== real plate

(-) imaginary charge

------------ imaginary plate

(+) imaginary charge
 
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  • #2
dimensionless said:
Does the bottom plate, along with the imaginary charge get reflected across the plate above the real charge?
Yes. In short, you can do the mirroring in steps. This will ultimately lead to an infinite chain of charges as described in your post.
 

1. What is the Method of Images Charges?

The Method of Images Charges is a mathematical technique used to solve electrostatic problems involving conductors and insulators. It involves creating a fictitious system of charges that replicates the boundary conditions of the original problem, and using the principle of superposition to solve for the electric potential and field.

2. When is the Method of Images Charges used?

The Method of Images Charges is commonly used in electrostatics problems involving conductors and insulators, such as finding the electric field and potential of a point charge near a conducting plane or a point charge near a grounded conducting sphere.

3. How does the Method of Images Charges work?

The Method of Images Charges works by creating a mirror image of the original charge or charges, called the "image charges," and placing them symmetrically with respect to a grounded conductor or an insulator. The sum of the electric potential and field due to the original charges and the image charges satisfies the boundary conditions of the problem, allowing for an accurate solution.

4. What are the advantages of using the Method of Images Charges?

The Method of Images Charges is a useful tool for solving electrostatic problems because it provides an analytical solution that is often easier and faster to calculate than other methods, such as numerical methods. It is also intuitive and can provide insight into the behavior of electric fields and potentials in different configurations.

5. Are there any limitations to the Method of Images Charges?

While the Method of Images Charges is a valuable tool, it does have some limitations. It can only be used for static cases and cannot account for time-varying or magnetic effects. It also assumes that the conducting or insulating surfaces are perfect and have no imperfections or irregularities.

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