Weird Plate Capacitor: Calculating Capacitance

• shomey
I have the feeling I got the first two sections wrong...something about my dealing with the dielectrics. could you have a look and tell me what you think?

Homework Statement

I have a capacitor which i just like a plate capacitor, but instead of the upper electrode being a plate it is a point charge Q. the lower plate is held at a fixed potential V=0.

I am supposed to calculate the capacitance of the capacitor.

The Attempt at a Solution

I've used the image method with a negative charge (-Q) at the same distance from the lower plate (forcing V=0 on this plate).
now I wanted to calculate the potential difference between the "plates", but it is obvisously inifinite since as we get closer to the point charge the potential grows like 1/x^2.
and thus C = Q/delta_V = 0
what am I missing?

thanks :)

shomey said:

Homework Statement

I have a capacitor which i just like a plate capacitor, but instead of the upper electrode being a plate it is a point charge Q. the lower plate is held at a fixed potential V=0.

I am supposed to calculate the capacitance of the capacitor.

The Attempt at a Solution

I've used the image method with a negative charge (-Q) at the same distance from the lower plate (forcing V=0 on this plate).
now I wanted to calculate the potential difference between the "plates", but it is obvisously inifinite since as we get closer to the point charge the potential grows like 1/x^2.
and thus C = Q/delta_V = 0
what am I missing?

thanks :)

someone? even if you are not sure I will be glad to hear what you think...

I looks to me like you are right. If one of the plates is an ideal point, you are going to have a really hard time shoving any charge into that capacitor. I'll vote for C=0.

Dick said:
I looks to me like you are right. If one of the plates is an ideal point, you are going to have a really hard time shoving any charge into that capacitor. I'll vote for C=0.

thanks.
I'll let you know how it goes...

shomey said:
thanks.
I'll let you know how it goes...

actually I'm pretty confused, so I'll try to work on it for a little while and let you know if I made some progress and/or have any questions.

thanks for the help!
shomey

shomey said:
actually I'm pretty confused, so I'll try to work on it for a little while and let you know if I made some progress and/or have any questions.

thanks for the help!
shomey

I solved the question, it's not that difficult after all - just a lot of calculations.
solution is attached if you are interested :) if you see an error i would love to know about it..

now - supposed I know the capacitance and the force felt by the upper electrode, and I know all dielectric coefficients eps_k, could I derive the dielectric layers' lengths??

I can see only two equations, thus missing (N-2) to solve the problem, but I was told it is possible...

Attachments

• problem.doc
145.5 KB · Views: 168
Last edited:
shomey said:
I solved the question, it's not that difficult after all - just a lot of calculations.
solution is attached if you are interested :) if you see an error i would love to know about it..

now - supposed I know the capacitance and the force felt by the upper electrode, and I know all dielectric coefficients eps_k, could I derive the dielectric layers' lengths??

I can see only two equations, thus missing (N-2) to solve the problem, but I was told it is possible...

I've made progress, I'm stuck with 6/8 equations, could you think about anything I might have missed? thanks!

Attachments

• problem.doc
167.5 KB · Views: 181
shomey said:
I've made progress, I'm stuck with 6/8 equations, could you think about anything I might have missed? thanks!

I have the feeling I got the first two sections wrong...
something about my dealing with the dielectrics.
could you have a look and tell me what you think?