# Weird plate capacitor

## 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 :)

## 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...

Dick
Science Advisor
Homework Helper
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.

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've wrote in email to my lecturer asking about it.
I'll let you know how it goes...

thanks.
I've wrote in email to my lecturer asking about it.
I'll let you know how it goes...

Okey so my lecturer had answered to use a small radius spherical electrode instead of a point charge.
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

Okey so my lecturer had answered to use a small radius spherical electrode instead of a point charge.
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: 113
Last edited:
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: 133
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?