R. (c) Calculate the total electric field energy associated with the charged sphere. (d) How much work is required to assemble the charge Q on the sphere? (e) Use the result of part (c) to find the capacitance of the sphere. (You can think of the second conductor as a hollow conducting shell of infinite radius.) (Figure 1) distance r from the center IDENTIFY and SET UP To find U, total electric-field energy, consider a spherical shell of radius r and thickness dr that has volume dV = 4rr dr. (It will help to make a drawing of such a shell concentric with the conducting sphere). The energy stored in this volume is udV, and the total energy is the integral of udV from r = 0 to r → 00. Part A Find the energy density of electric field u(r) in cases whenrR Express your answer in terms of some, all, or none of the variables Q, r, electric constant eg, and T separated by a comma. • View Available Hint(s) ΑΣφ u(r < R), u(r > R) = Figure < 1 of 1 > Submit Part B Complete previous part(s) EXECUTE R-> Part C Complete previous part(s) Part D Complete previous part(s)

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Chapter1: Units, Trigonometry. And Vectors
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<Ch 24 HW
Bridging Problem: Electric-Field Energy and Capacitance of a Conducting Sphere
12 of 15
I Review | Constants
A solid conducting sphere of radius R carries a charge Q. Calculate
the electric-field energy density at a point
of the sphere for (a) r < Rand (b) r > R. (c) Calculate the total
electric field energy associated with the charged sphere. (d) How
much work is required to assemble the charge Q on the sphere? (e)
Use the result of part (c) to find the capacitance of the sphere. (You
can think of the second conductor as a hollow conducting shell of
infinite radius.) (Figure 1)
distance r from the center
IDENTIFY and SET UP
To find U, total electric-field energy, consider a spherical shell of radius r and thickness dr that has volume dV = 4rr dr. (It will help to make a drawing of such a shell
concentric with the conducting sphere). The energy stored in this volume is udV, and the total energy is the integral of udV from r = 0 to r → 00.
Part A
Find the energy density of electric field u(r) in cases whenr<Rand r >R
Express your answer in terms of some, all, or none of the variables Q, r, electric constant eg, and T separated by a comma.
• View Available Hint(s)
ΑΣφ
u(r < R), u(r > R) =
Figure
< 1 of 1 >
Submit
Part B Complete previous part(s)
EXECUTE
R->
Part C Complete previous part(s)
Part D Complete previous part(s)
Transcribed Image Text:<Ch 24 HW Bridging Problem: Electric-Field Energy and Capacitance of a Conducting Sphere 12 of 15 I Review | Constants A solid conducting sphere of radius R carries a charge Q. Calculate the electric-field energy density at a point of the sphere for (a) r < Rand (b) r > R. (c) Calculate the total electric field energy associated with the charged sphere. (d) How much work is required to assemble the charge Q on the sphere? (e) Use the result of part (c) to find the capacitance of the sphere. (You can think of the second conductor as a hollow conducting shell of infinite radius.) (Figure 1) distance r from the center IDENTIFY and SET UP To find U, total electric-field energy, consider a spherical shell of radius r and thickness dr that has volume dV = 4rr dr. (It will help to make a drawing of such a shell concentric with the conducting sphere). The energy stored in this volume is udV, and the total energy is the integral of udV from r = 0 to r → 00. Part A Find the energy density of electric field u(r) in cases whenr<Rand r >R Express your answer in terms of some, all, or none of the variables Q, r, electric constant eg, and T separated by a comma. • View Available Hint(s) ΑΣφ u(r < R), u(r > R) = Figure < 1 of 1 > Submit Part B Complete previous part(s) EXECUTE R-> Part C Complete previous part(s) Part D Complete previous part(s)
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