Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vab = Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/ao0 + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-fb/a0 - efalao) + B In( ) + bo ( ))

Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rp has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = ae-r/ao + B/r + bo where alpha (a), beta (B), ao and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vab = Edr Calculating the antiderivative or indefinite integral, Vab = (-aage-r/ao0 + B + bo By definition, the capacitance C is related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C = Q/( (e-fb/a0 - efalao) + B In( ) + bo ( ))

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter28: Current And Resistance

Section: Chapter Questions

Problem 69PQ

See similar textbooks

Similar questions

A glass rod that has been charged to +12.0 nC touches a metal sphere. Afterward, the rod’s chargeis +8.0 nC. In both cases the fractional uncertainty is 1%. a. What kind of charged particle was transferred between the rod and the sphere, and in whichdirection? That is, did it move from the rod to the sphere or from the sphere to the rod? b. How many charged particles were transferred? Give full explanations
Solar wind is a flow of heavily charged ions emanating from the Sun’s corona. Spectroscopic analysis suggests it contains a density of approximately 5.0 electrons per cubic centimeter (cm3). Given that the elementary charge ? ≈ 1.6 × 10−19 ? and using the combined average of your measured values of Q, determine the charge density of a cubic meter (m3) of solar wind sample as a function of Q
In Millikan’s experiment, an oil drop of radius 1.64 mm and density 0.851 g/cm3 is suspended in chamber C when a downward electric field of 1.92 * 10^5 N/C is applied. Find the charge on the drop, in terms of e.
Assuming the radius of the circular path of the electron is 4.9cm when voltage is 100v and coil current is 1.4 A and The Helmholtz coils have 130 turns and a radius of 15 cm. With N=130 and R=0.15 If the current in the Helmholtz coils were 1.4 A, rather than 1 A, and the accelerating voltage were still 100 V, what would the radius of the electron's path be? Give your answer in cm, and enter only the number. Blackboard will accept an answer witin 20% of the value it expects.
A simple and common technique for accelerating electrons is shown in the figure, which depicts a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to pass through. Randomized Variables E = 2.7 × 104 N/C Calculate the horizontal component of the electron's acceleration if the field strength is 2.7 × 104 N/C. Express your answer in meters per second squared, and assume the electric field is pointing in the negative x-direction as shown in the figure.
In a cathode-ray tube (CRT), an electron travels in a vacuum and enters a region between two "deflection" plates which have equal and opposite charges. The dimensions of each plate are L = 12 cm by d = 5 cm, and the gap between them is h = 2.5 mm. (Note: the diagram is not drawn to scale and the direction of the electric field may not be correct, depending on your randomization.) During a 0.001 s interval while it is between the plates, the change of the momentum of the electron ΔP is < 0, 9.60e-17, 0 > kg m/s.What is the electric field between the plates?
If a proton and electron are released when they are 2.0 m apart, find the initial acceleration of electron (in m/s2). The answer (in fundamental SI unit) is ___________
In Millikan oil drop experiment, a negatively charged oil droplet of mass 3 × 10−12 g and charge 1.6 × 10−16C is kept suspended within the chamber. What is the electric field required to move the charge vertically downward atan acceleration of 5 cm/s 2 ?
How much charge (measured in C) does a conductor have if it contains 32 quintillion electrons?
A simple and common technique for accelerating electrons is shown in the figure, which depicts a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to pass through.Randomized VariablesE = 2.7 × 104 N/C Calculate the horizontal component of the electron's acceleration if the field strength is 2.7 × 104 N/C. Express your answer in meters per second squared, and assume the electric field is pointing in the negative x-direction as shown in the figure.
With what kinetic energy, in eV , must a proton be launched from the negative plate if it is just barely able to reach the positive plate? A parallel-plate capacitor with a 4.7 mm plate separation is charged to 78 V.
f a proton and electron are released when they are 2.0 m apart, find the initial acceleration of electron (in m/s2). The answer (in fundamental SI unit) is ___________ (type the numeric value only)