Charge induced on parallel plates if a charge between plates

[Rakesh Kumar Jaiswal]

Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate.

Many of the places this problem has been solved by considering an infinitely large plate in place of the point charge. This solution is also given in the Irodov book itself. I get the answer by this assumption but I don't understand this assumption fully. I have tried a lot to find any alternate method to solve this problem but could not get one. Now I am posting here with a lot of hope that somebody would certainly help me out.

Can anybody solve this question by any alternate method?

 

[PeroK]

Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate.

Many of the places this problem has been solved by considering an infinitely large plate in place of the point charge. This solution is also given in the Irodov book itself. I get the answer by this assumption but I don't understand this assumption fully. I have tried a lot to find any alternate method to solve this problem but could not get one. Now I am posting here with a lot of hope that somebody would certainly help me out.

Can anybody solve this question by any alternate method?

One solution would be to use the method of images. But, in this case, you will need an infinite sequence of image charges in both directions.

Using Green's reciprocation theorem is another approach.

 

[Rakesh Kumar Jaiswal]

One solution would be to use the method of images. But, in this case, you will need an infinite sequence of image charges in both directions.

Using Green's reciprocation theorem is another approach.

Thanks ReroK

I have tried to solve this by image method also but could not get the answer. At the limiting case (boundary conditions) I get equal charges induced on both plates.

Would you please solve this for me?

 

[PeroK]

Thanks ReroK

I have tried to solve this by image method also but could not get the answer. At the limiting case (boundary conditions) I get equal charges induced on both plates.

Would you please solve this for me?

I'm afraid, we can't just do your homework.

For what it's worth, I suspect the image method is quite hard. Quite complicated algebraically, at least.

 

[Rakesh Kumar Jaiswal]

I'm afraid, we can't just do your homework.

For what it's worth, I suspect the image method is quite hard. Quite complicated algebraically, at least.

Many people says this problem can be solved by image method but I could not find one who could actually solve this.

I am a physics faculty and I do my homework. It is long waited question to be solved for me. Please help me if you can.

 

[PeroK]

Many people says this problem can be solved by image method but I could not find one who could actually solve this.

I am a physics faculty and I do my homework. It is long waited question to be solved for me. Please help me if you can.

Well, I found at least one solution just by searching:

"method of images two parallel planes"

Although it seems that the method of images leads to an infinite series that cannot be simplified.

I also found a solution based on the Green reciprocation theorem, which looks like the way to go.

 

[haruspex]

Well, I found at least one solution just by searching:

"method of images two parallel planes"

Although it seems that the method of images leads to an infinite series that cannot be simplified.

I also found a solution based on the Green reciprocation theorem, which looks like the way to go.

The question asks for

Find the charges induced on each plate.

I take that as meaning the induced charge distribution. Do those methods answer that or only find the field/potential?

 

[PeroK]

The question asks for

I take that as meaning the induced charge distribution. Do those methods answer that or only find the field/potential?

The Green method finds the charge distribution. I searched for "two infinite grounded conducting planes". It's problem 1.13 from Jackson.

The method of images solution I found was looking for the force on the particle.