A nonconducting spherical shell, with an inner radius of 4 cm and an outer radius of 6 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density p is the charge per unit volume, with the unit coulomb per cubic meter. For this shell p = b/r, where r is the distance in meters from the center of the shell and b = 3 µC/m?. What is the net charge in the shell?

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Chapter1: Units, Trigonometry. And Vectors
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Hello,

   I understand that to calculate the net charge in the shell, I need to integrate the equation from 4 cm to 6 cm with volume charge density times 2 * pi * r * dr. However, since the problem here provides me with a novel expression of p = b/r, I am a bit lost... Could you please tell me how I can solve such problem?

A nonconducting spherical shell, with an inner radius of 4 cm and an outer radius of 6 cm,
has charge spread nonuniformly through its volume between its inner and outer surfaces.
The volume charge density p is the charge per unit volume, with the unit coulomb per
cubic meter. For this shell p = b/r, where r is the distance in meters from the center of the
shell and b = 3 µC/m?. What is the net charge in the shell?
Transcribed Image Text:A nonconducting spherical shell, with an inner radius of 4 cm and an outer radius of 6 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density p is the charge per unit volume, with the unit coulomb per cubic meter. For this shell p = b/r, where r is the distance in meters from the center of the shell and b = 3 µC/m?. What is the net charge in the shell?
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