- #1
stunner5000pt
- 1,461
- 2
A hollow spherical shell carries a charge density
[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... isn't charge density given in coulombs per cubic metre usually??
what I am 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!
[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... isn't charge density given in coulombs per cubic metre usually??
what I am 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!