Is There an Easier Method to Solve Problems Involving Image Charges?

[Saitama]

Homework Statement

(see attachment)

Homework Equations

The Attempt at a Solution

I think i need to use method of image charges here but if i do that, i need to place infinite fictitious charges and finding the electric field at the surface of any of the plate would be very difficult. Is there any easier method to solve this problem?

 

[aralbrec]

The Attempt at a Solution

I think i need to use method of image charges here but if i do that, i need to place infinite fictitious charges and finding the electric field at the surface of any of the plate would be very difficult. Is there any easier method to solve this problem?

Edit:

Sorry Pranav in my haste there I thought you had made a mistake when it was me. There is an infinite sequence of image charges. I would be tempted to do an infinite series summation of the voltage on each plate. Other than that nothing simpler is coming to my mind... maybe someone else will have an idea.====

The method of images is the right way to go if you can assume the plates are grounded.

You will only have to place a few charges (more than two!), not an infinite number. This is because you know the E field will be perpendicular to the plates (edit: at the plates!). So if you have a + charge located at distance x from plate 1, placing a - charge a distance x below plate 1 will generate an E field perpendicular to plate 1 at plate 1. Then look at the E field caused by that charge at distance x on plate 2. Another - charge placed can cause that E field to be perpendicular to plate 2.

The trickier bit is you are not done yet. This is because the new charges you placed cause E fields on the opposite plate. So the -ve charge you placed for plate 1 will also cause a field on plate 2. How would you go about making sure the field it causes on plate 2 is also perpendicular to plate 2?

 

[Saitama]

The method of images is the right way to go if you can assume the plates are grounded.

You will only have to place a few charges (more than two!), not an infinite number. This is because you know the E field will be perpendicular to the plates (edit: at the plates!). So if you have a + charge located at distance x from plate 1, placing a - charge a distance x below plate 1 will generate an E field perpendicular to plate 1 at plate 1. Then look at the E field caused by that charge at distance x on plate 2. Another - charge placed can cause that E field to be perpendicular to plate 2.

The trickier bit is you are not done yet. This is because the new charges you placed cause E fields on the opposite plate. So the -ve charge you placed for plate 1 will also cause a field on plate 2. How would you go about making sure the field it causes on plate 2 is also perpendicular to plate 2?

How does this help in making the problem any easier?

This question is from the problem book by I.E.Irodov. I have a book written by him "Basic laws of electromagnetism". This book has a solved problem similar to this one. In that, the author replaces the charge with a uniformly charged plane parallel to the plates. I would like to know why this is valid.

 

[Saitama]

Anyone?

 

[ehild]

Read this: http://physicspages.com/2012/04/02/greens-reciprocity-theorem/

ehild

 

[Saitama]

Read this: http://physicspages.com/2012/04/02/greens-reciprocity-theorem/

ehild

One of the similar threads at PF redirected me to Green Reciprocity Theorem. I tried to study it but I can't understand it. This isn't too much necessary for my current syllabus, moreover method of image charges is also not in my syllabus. I was doing this as an additional exercise, this is the only problem i had difficulty with. Thanks for the help anyways.