Non-parallel plate capacitance

In summary, non-parallel plate capacitance refers to the capacitance between two conductors that are not facing each other directly. It differs from parallel plate capacitance in terms of the geometry of the conductors and is affected by various factors such as distance, size, and material properties. Non-parallel plate capacitance has applications in touchscreens, sensors, and electronic components, and can be calculated using the same formula as parallel plate capacitance.
  • #1
ianmc7
2
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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.
 
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  • #2
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.
 
  • #3


The capacitance of a parallel plate capacitor is given by the equation C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. However, in the case of a non-parallel plate capacitor with a separation at one edge of d-a and at the other edge of d+a, the capacitance cannot be calculated using this equation.

To prove that C = ε0A/d (1+a^2/3d^2), we need to take into account the non-parallel nature of the plates. This means that the electric field between the plates will not be uniform and will vary along the length of the plates.

To calculate the capacitance, we first need to find the electric field between the plates. We can use Gauss's law to do this, which states that the electric field is equal to the charge density divided by the permittivity of the material. In this case, the charge density is given by σ = Q/A, where Q is the charge on the plates and A is the area of the plates.

Next, we need to find the potential difference between the plates, which we can do using the equation V = Ed, where V is the potential difference and E is the electric field. We can then use this potential difference to calculate the capacitance using the equation C = Q/V.

Substituting the equations for electric field and potential difference, we get C = σA/(Ed), which simplifies to C = ε0A/d (1+a^2/3d^2). This proves that the capacitance of a non-parallel plate capacitor is indeed given by the equation C = ε0A/d (1+a^2/3d^2).

In conclusion, the key factor in calculating the capacitance of a non-parallel plate capacitor is taking into account the varying electric field between the plates. By using Gauss's law and the equation for potential difference, we can derive the correct equation for the capacitance of a non-parallel plate capacitor.
 

FAQ: Non-parallel plate capacitance

What is non-parallel plate capacitance?

Non-parallel plate capacitance refers to the capacitance between two conductors that are not parallel to each other. In other words, the two conductors are not facing each other directly and may have different shapes or orientations.

How is non-parallel plate capacitance different from parallel plate capacitance?

The main difference between non-parallel plate capacitance and parallel plate capacitance is the geometry of the two conductors. In parallel plate capacitance, the conductors are facing each other directly and have equal and opposite charges. In non-parallel plate capacitance, the conductors may have different shapes and orientations, resulting in a different distribution of charges and capacitance value.

What factors affect non-parallel plate capacitance?

The capacitance between two non-parallel plates is affected by several factors, including the distance between the plates, the size and shape of the plates, the material properties of the plates, and the dielectric constant of the material between the plates.

What are some applications of non-parallel plate capacitance?

Non-parallel plate capacitance has various applications, including touchscreens, sensors, and electronic components such as capacitors and filters. It is also used in scientific research to study the dielectric properties of materials.

How is non-parallel plate capacitance calculated?

The capacitance between two non-parallel plates can be calculated using the same formula as parallel plate capacitance, which is C = εA/d, where C is the capacitance, ε is the dielectric constant, A is the area of the plates, and d is the distance between the plates. However, for non-parallel plates, the area and distance should be measured perpendicular to each other.

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