Problem 6. Calculate the amount of electrostatic energy of a uniform sphere of charge in vacuum with radius b and volume charge density p stored in the following regions: b Hint: use, W== 1/2 [ « E² dv (J). RdR (a) Inside the sphere (b) Outside the sphere (c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating W = [dw = [vdq, where v is an intermediate scalar potential when dq is assembled. (Hint. Discretize the sphere into sum of thin spherical shells of thickness dR, then integrate) (d) Compare the results of (a), (b) and (c) and find the relation between them.
Problem 6. Calculate the amount of electrostatic energy of a uniform sphere of charge in vacuum with radius b and volume charge density p stored in the following regions: b Hint: use, W== 1/2 [ « E² dv (J). RdR (a) Inside the sphere (b) Outside the sphere (c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating W = [dw = [vdq, where v is an intermediate scalar potential when dq is assembled. (Hint. Discretize the sphere into sum of thin spherical shells of thickness dR, then integrate) (d) Compare the results of (a), (b) and (c) and find the relation between them.
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Problem 6. Calculate the amount of electrostatic energy of a uniform sphere of charge in vacuum with
radius b and volume charge density p stored in the following regions:
Hint: use,
W₂ =
{
[ € E² dv
(J).
b
RdR
(a)
Inside the sphere
(b)
Outside the sphere
(c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating
w = [dw = [vdq, where v is an intermediate scalar potential when dq is assembled.
P
(Hint. Discretize the sphere into sum of thin spherical shells of thickness dR, then integrate)
(d) Compare the results of (a), (b) and (c) and find the relation between them.
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