Non-parallel plate capacitance

  • Thread starter Thread starter ianmc7
  • Start date Start date
  • Tags Tags
    Capacitance Plate
AI Thread Summary
Calculating the capacitance of a non-parallel plate capacitor with varying separation requires integrating the voltage over the distance between the plates. The distance is defined as x=d+ay/L, where a is a small deviation from the average separation d. The goal is to prove that the capacitance C can be expressed as C= epsilon_not A/d (1+a^2/3d^2). The approach involves integrating V/(d+ay/L) from y=-L/2 to +L/2 and expanding the logarithm to simplify the expression. This method provides a pathway to derive the desired capacitance formula.
ianmc7
Messages
2
Reaction score
0
Im having trouble calculating the capacitance of a non-parallel plate capacitor where separation at one edge is d-a and the other it is d+a, assuming a<<d. I'm supposed to prove that C= epsilon_not A/d (1+a^2/3d^2). Thanks for the help.
 
Physics news on Phys.org
The equations for the distance between the plates is x=d+ay/L.
The surface charge ~V/x.
Integrate V/(d+ay/L) from y=-L/2 to +L/2.
Expand the logarithm.
 

Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
View full post »
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
View full post »

Similar threads

Capacitance of parallel plate capacitor separated by
Replies
3
Views
1K
I Parallel plate capacitor, charge imbalance VS charge redistribution
Replies
1
Views
915
Inserting a conductor in a parallel-plate capacitor
Replies
2
Views
2K
Prove to me how capacitors in parallel can have the same V across plates
Replies
7
Views
2K
Sample smaller than parallel plates in capacitance setup
Replies
5
Views
2K
Inserting metal to parallel plate capacitor
Replies
2
Views
8K
I Capacitor connected to voltage source, vary plate separation
Replies
9
Views
2K
I Capacitor surface charge movement current, relativistic effects
Replies
2
Views
1K
Why does a single sphere have a capacitance?
Replies
9
Views
5K
I Speed of Electricity in Plate Capacitor & Cable
Replies
18
Views
2K

Hot Threads

Recent Insights

Back
Top