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Problem 6. Calculate the amount of electrostatic energy of a uniform sphere of charge in vacuum with radius $b$ and volume charge density $ ho$ stored in the following regions: Hint: use, $W_e = frac{1}{2} int_v epsilon E^2 ,dV$ (J). (a) Inside the sphere (b) Outside the sphere (c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating $W_e = int dW_e = int v dq$, 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 $
ho$ stored in the following regions:
Hint: use, $W_e = frac{1}{2} int_v epsilon E^2 ,dV$ (J).
(a) Inside the sphere
(b) Outside the sphere
(c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating
$W_e = int dW_e = int v dq$, 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.

$Problem 6. Calculate the amount of electrostatic energy of a uniform sphere of charge in vacuum with radius b and volume charge density ho stored in the following regions: Hint: use, We = frac12 intv epsilon E^2 ,dV (J). (a) Inside the sphere (b) Outside the sphere (c) Calculate the total electrostatic energy to assemble this uniform sphere, by calculating We = int dWe = int v dq, where v is an intermediate scalar potential when dq is assembled. (Hint. Discretize the sphere into sum of thin spherical shells of thickness dR, then integrate) (d) Compare the results of (a), (b) and (c) and find the relation between them.$

Added by Felix P.

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