How to Calculate Capacitance for Two Slanted Conducting Plates?

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SUMMARY

The capacitance of two slanted conducting plates can be calculated using the formula C = (εA)/d, where ε is the permittivity, A is the area, and d is the distance between the plates. In this discussion, the plates have dimensions of 10x20 cm and 10x(20sec30) degrees. The approach involves integrating the capacitance of differential strips of the plates, with the distance d' varying based on the angle θ. The numerical values provided in the problem were incorrect, as one end of the slanted plate is 1 mm from the top plate, while the other end is 0.1 mm, leading to a tan θ calculation of 0.9 mm/0.1 mm, which does not equal tan(30).

PREREQUISITES
  • Understanding of capacitance and the formula C = (εA)/d
  • Familiarity with integration techniques in calculus
  • Knowledge of trigonometry, specifically tangent functions
  • Basic concepts of electric fields and permittivity
NEXT STEPS
  • Study the derivation of capacitance for non-parallel plate configurations
  • Learn about the integration of functions in calculus, particularly in physics applications
  • Explore the implications of slanted plates on electric field distribution
  • Investigate numerical methods for solving capacitance problems with varying geometries
USEFUL FOR

Physics students, electrical engineers, and anyone involved in capacitor design or analysis of electric fields in non-standard geometries.

blackblanx
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Homework Statement



Determine the capacitance of two conducting plates facing each other at an angle as shown (in link) . Plate A and B have dimensions of 10x20 cm and 10x (20sec30) (angles in degrees)

Homework Equations


C=( \epsilon A)/d


The Attempt at a Solution


not quite sure can someone help me get the ball rolling or the floor moving
 

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If you take one strip of the plate of width dx and length L.
The capacity of that strip is given by
ΔC = εο*L*dx/(d + d')
From the figure write down d' in terms of x and θ.
Find the integration to get the capacitance C.
 
What are you using for d' ?
 
blackblanx said:
What are you using for d' ?
d' is the variance distance of the slanted plate from the horizontal line.
In the problem, numerical values are not correct.
One end of the slanted plate is 1 mm from the top plate,. And the other end is 0.1 mm from the top plate. So tan θ = 0.9 mm/0.1 mm which is not equal to tan(30)
 

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