How Does Capacitance Change with Angle in Non-Parallel Plate Capacitors?

For a capacitor with square plates, each of side a and making an angle theta with each other, the capacitance is given by C = [(epsilon)(a^2)/d][1-(a(theta)/2d)] for small values of theta. This can be derived by dividing the strip into N segments, each with length a/N, and using the equation C = (epsilon)(a)(delta x)/y, where S = a(delta x) and d = y." In summary, the capacitance of a capacitor with square plates and small angles between them can be calculated using the equation C = [(epsilon)(a^2)/d][1-(a(theta)/2d)], where a is the side length of the
  • #1
Fusilli_Jerry89
159
0

Homework Statement


A capacitor has square plates, each of side a, making an angle theta with each other. Shown that for small theta the capacitance is given by: C = [(epsilon)(a^2)/d][1-(a(theta)/2d].


Homework Equations


C = q/V
gauss' law


The Attempt at a Solution


I see how you can divide up the strip into N segments each with length a/N. But how do u get the capacitance for each strip to be C = (epsilon)a(deltax)/y ? I know how to do the rest and I know for sure that that's the right way to do it, but how do u get the capacitance for each strip?)
 
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  • #2
See that C = [tex]\epsilon[/tex]*S/d, in your case for each strip S = a*dx and d = y.
 
  • #3
I'm also troubled with this question, I know it has been a long time, but maybe one of you can explain me the answer?

Omer
 

FAQ: How Does Capacitance Change with Angle in Non-Parallel Plate Capacitors?

What is a non-parallel plate capacitor?

A non-parallel plate capacitor is a type of capacitor in which the two plates are not parallel to each other. This means that the distance between the plates varies, which affects the capacitance of the capacitor.

How is the capacitance of a non-parallel plate capacitor calculated?

The capacitance of a non-parallel plate capacitor is calculated using the formula C = εA/d, where C is the capacitance, ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates.

What are the applications of non-parallel plate capacitors?

Non-parallel plate capacitors are used in various electronic devices such as sensors, filters, and tuning circuits. They are also used in power factor correction and energy storage systems.

How does the distance between the plates affect the capacitance of a non-parallel plate capacitor?

The distance between the plates has a direct impact on the capacitance of a non-parallel plate capacitor. As the distance decreases, the capacitance increases, and vice versa. This is because a smaller distance allows for a stronger interaction between the plates, resulting in a higher capacitance.

What are the advantages and disadvantages of non-parallel plate capacitors?

One advantage of non-parallel plate capacitors is that they can be designed to have a higher capacitance than parallel plate capacitors with the same surface area. However, their capacitance can be affected by factors such as temperature and humidity. Additionally, their non-parallel shape can make them more challenging to manufacture and may result in higher costs.

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