Calculating Capacitance and Electric Force in a System of Connected Capacitors

[shomey]

I'm trying to figure out the capacitance of the attached system.

may I look at this problem as N capacitors attached in a cascade connenction?

I'm also trying to figure out the force that will be felt by the point charge.
I thought about using the image method... could you thing of a better solution? I'm worried it will be very long and frustrating...

thanks!

 

[maverick280857]

Yes, all those are in series. You can replace them by a single capacitance.

I don't understand the statement "..and can be seen as a point charge Q". Do you mean to say that the charge on the capacitor plate is Q?

 

[shomey]

Yes, all those are in series. You can replace them by a single capacitance.

I don't understand the statement "..and can be seen as a point charge Q". Do you mean to say that the charge on the capacitor plate is Q?

Thanks very much for the help!

sorry for the bad explanation.
what i was told is that the electrode of the capacitor is a point charge Q.
I guess it means two things:
1. the charge on the capacitor's upper plate is Q.
2. the capacitor's upper plate is very small on the horizontal axises - which sounds very strange...

This leads me to my next question:

could there be a capacitor without two metal plates on its two ends?
It is not drawn on the picture I got (only N dielectric plates), but maybe I was supposed to assume that they are there...

Again - thanks very much for the help!

 

[shomey]

Thanks very much for the help!

sorry for the bad explanation.
what i was told is that the electrode of the capacitor is a point charge Q.
I guess it means two things:
1. the charge on the capacitor's upper plate is Q.
2. the capacitor's upper plate is very small on the horizontal axises - which sounds very strange...

This leads me to my next question:

could there be a capacitor without two metal plates on its two ends?
It is not drawn on the picture I got (only N dielectric plates), but maybe I was supposed to assume that they are there...

Again - thanks very much for the help!

Thought about it a little more and I guess what they've ment in the question is that the upper electrode could be considered a point charge when calculating the force it feels...

 

[shomey]

Hey guys!

I think I've solved it, attached is my solution.

I have some last little points I would love to understand better:

1) why is the field D contant though the capacitor? (I've read it in a notebook but could not understand why this is true - they've claimed it is because of the symmetry of the problem...)
2) In the solution I've calculated E_n using Gauss envelopes, and then saw that D is constant, how can I calculate D directly?
3) sometimes we write D=eps*E+P and sometimes we ommit P... why is that? how could I explain this?

thank you very much for the help!

 

[reilly]

Re 1&2. You have, for all practical purposes done a direct computation.Otherwise, look at the integral for the field, and you'll be direct, and 2, you'll see the important symmetry in action

Regards,
Reilly Atkinson