Capacitance and inductance of cylindrical shell

Mythe's "Static and Dynamic Electricity" textbook provides solutions for challenging cylindrical geometry capacitance and inductance problems, including off-center geometries. The inductance and capacitance per unit length, L and C, are related by the equation LC = εε0μμ0 = 1.11 x 10-17 εμ Farad-Henrys/meter2. This formula can be used to find the inductance and capacitance of a cylindrical shell with a gap, taking into account its inner and outer radii, as well as the filling dielectric and small gap.
  • #1
integralll
1
0
i am having trouble with finding inductance and capacitance of a cylindrical shell with gap.

say inner radius is a, outer radius is b, and filling dielectric between a and b,

and its not a exact circle which have a small gap say d. its like a split ring but only one shell.

How can i find C and F?
 
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  • #2
Smythe "Static and Dynamic Electricity" (third edition) has solutions for many difficult cylindrical geometry capacitance and inductance problems, including off-center geometries.

For these problems, if L is the inductance per unit length, and C is the capacitance per unit length, L and C are related by

LC = εε0μμ0 = 1.11 x 10-17 εμ Farad-Henrys/meter2

Bob S
 

What is capacitance and inductance of a cylindrical shell?

Capacitance and inductance are two important parameters used to measure the energy storage and transmission capabilities of a cylindrical shell. Capacitance refers to the ability of the shell to store electric charge, while inductance measures the ability of the shell to store magnetic energy.

How are capacitance and inductance calculated for a cylindrical shell?

Capacitance and inductance of a cylindrical shell can be calculated using the following equations:
Capacitance (C) = (2πεrL)/(ln(b/a))
Inductance (L) = (μ0/2π)ln(b/a)
Where ε is the permittivity of the material, r is the radius of the shell, L is the length of the shell, μ0 is the permeability of free space, and a and b are the inner and outer radii of the shell respectively.

What factors affect the capacitance and inductance of a cylindrical shell?

The capacitance and inductance of a cylindrical shell are affected by factors such as the material used, the geometry of the shell, and the frequency of the electric or magnetic field. The permittivity and permeability of the material also play a significant role in determining these parameters.

How does the capacitance and inductance of a cylindrical shell impact its performance?

The capacitance and inductance of a cylindrical shell play a crucial role in determining its ability to store and transmit energy. Higher capacitance allows for greater energy storage, while higher inductance allows for better transmission of energy. These parameters also affect the resonance frequency and impedance of the shell, which can impact its performance in different applications.

What are some real-world applications of capacitance and inductance of cylindrical shells?

Capacitance and inductance of cylindrical shells are important in various fields such as telecommunications, power transmission, and electronic circuits. They are also used in the design of electrical components such as capacitors and inductors, and in medical imaging devices like MRI machines.

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