A cylindrical air capacitor of length 15.0 m stores 3.20 ×10^-9 J of energy when the potential d

Name: Problem 33, Chapter 24: University Physics with Modern Physics
Uploaded: 2020-08-30T10:09:34-08:00
Duration: 4 min 55 s
Channel: Vishal Gupta
Description: A cylindrical air capacitor of length 15.0 m stores 3.20 ×10^-9 J of energy when the potential difference between the two conductors is 4.00 V . (a) Calculate the magnitude of the charge on each conductor. (b) Calculate the ratio of the radii of the inner and outer conductors.

step 1 In the given problem there is a cylindrical capacitor whose length is given as 15 .0 meter. The

A cylindrical air capacitor of length 15.0 m stores 3.20...

A cylindrical air capacitor of length 15.0 $\mathrm{m}$ stores $3.20 \times 10^{-9} \mathrm{J}$ of energy when the potential difference between the two conductors is 4.00 $\mathrm{V}$ . (a) Calculate the magnitude of the charge on each conductor. (b) Calculate the ratio of the radii of the inner and outer conductors.

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Key Concepts

Capacitors

Capacitors are electrical components that store energy in an electric field between two conductors separated by an insulating material. Their fundamental relationship is described by the equation Q = CV, where Q is the stored charge, C is the capacitance, and V is the voltage across the capacitor.

Energy Storage in Capacitors

The energy stored in a capacitor is given by U = ½CV². This equation allows one to relate the amount of energy stored to the capacitance and the voltage applied, making it crucial in determining either energy, capacitance, or charge in a system.

Cylindrical Capacitor Geometry

Cylindrical capacitors consist of two coaxial cylindrical conductors with the capacitance depending on the length of the cylinders and the ratio of their radii. The capacitance is expressed by the formula C = (2???L) / ln(b/a), where L is the length, b is the radius of the outer cylinder, a is the radius of the inner cylinder, and ?? is the permittivity of free space.

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