Electrodynamics Method of imaging

In summary, the method of image charges involves using opposite point charges to solve problems in physics, specifically for finding unique solutions to Laplace's equation. The example of a point charge above an infinite conducting plate is commonly used, but understanding the sphere example can be challenging. The Wikipedia article provides a helpful explanation, but the value of the mirror charge may not be immediately apparent. The mirror charge is chosen to cancel out the field from the original charge at a specific position, and its location and value can be determined by setting the potential to zero at a desired point. The process for determining the mirror charge involves using a free parameter to find the correct radius for the equipotential surface.
  • #1
sleventh
64
0
Hello all,

I have recently been taught the method of imagging with opposite point charges. The stereotypical example of a point charge above an infinit conducting plate comes fine but i can't grasp the sphere example. It is shown http://en.wikipedia.org/wiki/Method_of_image_charges" [Broken] , I can't see how they derive the value of the mirror charge, thank you very much any help is appreciated.

sleventh
 
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  • #2
Who knows? At least we know that the solution to Laplace's equation will be unique. How they came up with the image charge is probably a long and boring process. It could have just been that someone solved the problem by directly finding a solution to the associated Laplace equation and then noticed that you could decompose it into the summation of the charge and an image charge. Lots of times it seems that complicated relationships that can be distilled into more simplified physical situations are usually found after the fact by playing around with the results and trying to decompose them into more meaningful forms.

But apart from however they came up with the relationship, as long as we can prove that it satisifies Laplace's equation and the resulting boundary equations then we know it is the solution to the potential. This part is easier to show as they have done in the Wikipedia article.
 
  • #3
sleventh said:
Hello all,

I have recently been taught the method of imagging with opposite point charges. The stereotypical example of a point charge above an infinit conducting plate comes fine but i can't grasp the sphere example. It is shown http://en.wikipedia.org/wiki/Method_of_image_charges" [Broken] , I can't see how they derive the value of the mirror charge, thank you very much any help is appreciated.

sleventh

It is chosen so as to cancel exactly the field from q at the position R between the two charges.I.e. the position and value of the mirror charge is chosen to accomplish this. You can either have a large mirror charge far away, or a smaller charge closer by. So there is a free parameter that is chosen so that the system describes a sphere. If I assume that the mirror charge is located at R^2/p on the x-axis, I get for the mirror charge Q:

Cancellation of the potential at x=R:
q/(R-p) + Q/(R^2/p - R) = 0

Gives:
Q = -qR/p

In this I already assumed that the mirror charge would be located at R^2/p. If you want to derive this, you need to leave that as a free parameter, write down the total potential as they do, and then determine for which mirror charge position the V=0 equipotential surface is a sphere of the correct radius.

Torquil
 
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1. What is the Electrodynamics Method of imaging?

The Electrodynamics Method of imaging is a scientific technique used to create images of objects or materials by measuring the response of electromagnetic waves to those objects or materials. It is based on the principles of electromagnetism and can be used to study a wide range of materials, including biological tissues, electronic devices, and geological structures.

2. How does the Electrodynamics Method of imaging work?

The Electrodynamics Method of imaging works by sending electromagnetic waves, such as radio waves or microwaves, towards an object or material. These waves interact with the object, producing changes in their properties. These changes are then measured and used to create an image of the object or material.

3. What are the advantages of using the Electrodynamics Method of imaging?

The Electrodynamics Method of imaging has several advantages over other imaging techniques. It is non-invasive, meaning it does not require physical contact with the object or material being studied. It is also non-destructive, so it does not damage the object or material. Additionally, it can provide high-resolution images and can be used to study a wide range of materials.

4. What are some applications of the Electrodynamics Method of imaging?

The Electrodynamics Method of imaging has a variety of applications in different fields of science and technology. In medicine, it can be used for diagnostic imaging and studying the structure of tissues. In geology, it can be used to map underground structures and detect natural resources. In materials science, it can be used to study the properties of materials and identify defects. It is also used in the development of electronic devices and telecommunications.

5. Are there any limitations or challenges associated with the Electrodynamics Method of imaging?

While the Electrodynamics Method of imaging has many advantages, it also has some limitations and challenges. It requires specialized equipment and can be expensive to implement. The interpretation of the images can also be complex and may require expertise in both electromagnetism and the material being studied. Additionally, some materials may not be suitable for imaging using this method, as they may not produce a measurable response to electromagnetic waves.

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