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home / study / questions and answers / science / physics / a non-conducting spherical shell with an inner ... Question A non-conducting spherical shell with an inner radius of 0.04m and an outer radius of 0.05m has charge spread non-uniformly through its volume (between the inner and outer surfaces). The volume charge density p is the charge per unit volume and has units of coulomb/m^3. For this shell p = (3uC/m^2)/r, where "r" is the distance from the center of the shell. What is the net charge in the shell? (To find Q, you must integrate because the charge density is NOT uniform.)

im getting (3x10^-6)(2Pi)(0.05^2 - 0.04^2) or about 1.697 x 10^-8 C Correct?

Explanation / Answer

I think you are correct

from the relation dQ = p dV , dv volumeof spherical shell, p- volume charge density

now dV can be written as 4 pi r^2 dr

and net charge Q = integration of dQ betwee the limits from 0.05 m to 0.04 m

then Q = 2*pi*3*10^-6(0.05^2 - 0.04^2)
   = 1.6964600329385*10^-8 C

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