A spherical capacitor consists of a single conducting sphere of radius R = 12 cm that carries a positive charge Q = 55 nC. The capacitance forthis spherical capacitor is given by the equation C ='= 4περR.and eo.and &0.Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor. Write your equation in terms of R, Q,Use Gauss's law to write an equation for the electric field everywhere inside the spherical capacitor (r < R).Use Gauss's Law to write an equation for the radial electric field at a radius r outside the spherical capacitor. Give your answer in terms of Q, r,and 80.Write an equation for the energy density due to the electric field outside the spherical capacitor in terms of Q, r,Consider a thin spherical shell of thickness dr and radius r > R that is concentric with the spherical capacitor. Write an equation for the totalenergy contained in the shell in terms of Q, r, dr, and &o.Find the total energy stored in the field by integrating the energy over the radius outside the conducting shell. Write this total energy contained inthe shell in terms of Q, R, and EO.

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A spherical capacitor consists of a single conducting sphere of radius R = 12 cm that carries a positive charge Q= 55 nC. The capacitance for this spherical capacitor is given by the equation C = 4лER. and eg and &0- Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor. Write your equation in terms of R, Q, Use Gauss's Law to write an equation for the electric field everywhere inside the spherical capacitor (r R that is concentric with the spherical capacitor. Write an equation for the total energy contained in the shell in terms of Q, r, dr, and E. Find the total energy stored in the field by integrating the energy over the radius outside the conducting shell. Write this total energy contained in the shell in terms of Q, R, and E-

A spherical capacitor consists of a single conducting sphere of radius R = 12 cm that carries a positive charge Q= 55 nC. The capacitance for this spherical capacitor is given by the equation C = 4лER. and eg and &0- Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor. Write your equation in terms of R, Q, Use Gauss's Law to write an equation for the electric field everywhere inside the spherical capacitor (r R that is concentric with the spherical capacitor. Write an equation for the total energy contained in the shell in terms of Q, r, dr, and E. Find the total energy stored in the field by integrating the energy over the radius outside the conducting shell. Write this total energy contained in the shell in terms of Q, R, and E-

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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An electrostatic force is a force caused by stationary electric charges /fields. The electrostatic force is caused by the transfer of electrons in conducting materials. Coulomb’s law determines the amount of force between two stationary, charged particles. The electric force is the force which acts between two stationary charges. It is also called Coulomb force.

Question

A spherical capacitor consists of a single conducting sphere of radius R = 12 cm that carries a positive charge Q = 55 nC. The capacitance for
this spherical capacitor is given by the equation C =
'= 4περR.
and eo.
and &0.
Write an equation for the energy stored in a spherical capacitor when a charge Q is placed on the capacitor. Write your equation in terms of R, Q,
Use Gauss's law to write an equation for the electric field everywhere inside the spherical capacitor (r < R).
Use Gauss's Law to write an equation for the radial electric field at a radius r outside the spherical capacitor. Give your answer in terms of Q, r,
and 80.
Write an equation for the energy density due to the electric field outside the spherical capacitor in terms of Q, r,
Consider a thin spherical shell of thickness dr and radius r > R that is concentric with the spherical capacitor. Write an equation for the total
energy contained in the shell in terms of Q, r, dr, and &o.
Find the total energy stored in the field by integrating the energy over the radius outside the conducting shell. Write this total energy contained in
the shell in terms of Q, R, and EO.

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A spherical capacitor consists of an inner spherical shell of radius R1 and an outer spherical shell of radius R2, as shown above. Our goal is to calculate the capacitance of this configuration of electrodes.To start, suppose the inner sphere has a charge +Q and the outer sphere an equal but opposite charge -Q. Find the capacitance using the following steps:1. Use Gauss's law to find an expression for the electric field in the region between the two spheres.2. Find an expression for the potential difference between the spheres from the electric field (you'll have to integrate the electric field from the negative electrode to the positive one).3. Calculate the capacitance from C = Q / ΔV.Suppose in this case that R1 = 2.00 cm and R2 = 4.30 cm. What is the value of the capacitance?