A hollow spherical shell carries a charge density(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \rho = \frac{k}{r^2} [/tex]

in the region a<= r <= b. As in the figure

Find the elctric field in these three regions

i) r <a

ii) a<r<b

iii) r>b

SOlution:

for r<a it simple.. no exclosed charge for any gaussian sphere within that region so E = 0

for a<r<b

the thing which stumps is the charge density... isnt charge density given in coulombs per cubic metre usually??

what im concerned about in the enclosed charge in teh gaussian sphere of radius a<r<b... would i integrate rho from r' = a to r' = r??

rho dot dr would give the total charge enclosed, no??

doing that gives

[tex] q_{enc} = k\left(\frac{1}{a} - \frac{1}{r}\right) [/tex]

[tex] E (4 \pi r^2) = \frac{k}{epsilon_{0}} \left(\frac{1}{a} - \frac{1}{r}\right)

for the third part that is r>b would i do something similar but integrate from r' =a to r'=b??

Please help!

Help is always greatly appreciated!

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# Homework Help: Gauss Law

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