If I have a sphere with radius R which has a charge distribution given by
[itex]\rho(r)=\frac{5Q}{\pi R^{5}}r(r-R)[/itex]
and [itex]\rho = 0 [/itex] at r bigger or equal to R, how do I find the electrostatic potential of this overall space? There is a charge Q, in addition, at the origin.
My original thought was to just do the usual and use
[itex]V(r)=\frac{1}{4\pi\epsilon_{0}}\int \frac{\rho(r')}{r}dt'[/itex],
which if I am correct the integration goes from 0 to R, correct. Or does it extend from infinity in to R? This has never made much sense to me. Somebody help me out with this idea. Thanks!
[itex]\rho(r)=\frac{5Q}{\pi R^{5}}r(r-R)[/itex]
and [itex]\rho = 0 [/itex] at r bigger or equal to R, how do I find the electrostatic potential of this overall space? There is a charge Q, in addition, at the origin.
My original thought was to just do the usual and use
[itex]V(r)=\frac{1}{4\pi\epsilon_{0}}\int \frac{\rho(r')}{r}dt'[/itex],
which if I am correct the integration goes from 0 to R, correct. Or does it extend from infinity in to R? This has never made much sense to me. Somebody help me out with this idea. Thanks!