- #36
Chopin
- 368
- 13
Looks right to me. You're in the home stretch now..."finish him"!
l1fesavers said:Now you mentioned that I still need to include the original line charge so that would be something like:
[itex]Q_{enc} = Q_{1} + Q_{2} [/itex] where Q1 was line charge and Q2 was the cylindrical shell?
l1fesavers said:Going through the process for Region III again but this time including the line charge netted me this:
[tex]E = \dfrac{\alpha(b^3-a^3)+\lambda}{3 \epsilon_{o} r}[/tex]
l1fesavers said:That the net result of several fields is the summation of the result of each individual field?
l1fesavers said:As for region 2, the field that is enclosed is the volume of the hollowed out cylindrical shell?
l1fesavers said:So for Region 2
[tex] E = \dfrac{\lambda}{2\pi r \epsilon_{o}} + \dfrac{\alpha(b^3-a^3)}{3 \epsilon_{o} r}[/tex]
l1fesavers said:Region II does not include the entire cylinder - it only includes up until our Gaussian surface, so it goes to 'r'...
[tex] E = \dfrac{\lambda}{2\pi r \epsilon_{o}} + \dfrac{\alpha(r^3-a^3)}{3 \epsilon_{o} r}[/tex]
l1fesavers said:It does, so...
[tex] E = \dfrac{\lambda}{2\pi r \epsilon_{o}} + \dfrac{\alpha(b^3-a^3)}{3 \epsilon_{o} r}[/tex]
l1fesavers said:Thanks so much to both of you for your amazing help! And even more amazing level of patience with both my ignorance and extremely rusty math haha