 #1
 20
 0
i have a hemispherical shell with a radius of R ,and which has V=V_{0} potential on it. the main problem is i have to find the potential inside the shell for every (r,[tex]\theta[/tex],[tex]\phi[/tex]) points.
1. I think the potential will depent on only the distance from origin, there won't be any [tex]\theta[/tex] or [tex]\phi[/tex] in the equation. on the other hand, if has a charge on it not a potential, inside the shell potential would be constant. So, is it gonna be constant or not in this situation?
2. my attemp to find the potential inside shell is:
i will find the potential on P point (shown in the picture)
V(P)=k[tex]\int[/tex] [tex]\sigma[/tex] dS / r
r=(s^{2}+R^{2}2Rscos[tex]\theta[/tex])^{1/2}
dS=R^{2}sin[tex]\theta[/tex] d[tex]\theta[/tex]d[tex]\phi[/tex]
for a hemispherical shell [tex]\theta[/tex]=0pi (?) and [tex]\phi[/tex] = 02pi
if i put them in the integral and solve it the result is V(p)=2 [tex]\pi[/tex] kR [tex]\sigma[/tex] (sR)/(s)
if this is right, i can use V_{0} and find the result in terms of V_{0}. now if anyone can tell me if this is right or wrong i can continue, i will simulate this event and i really appreciate if anyone help me.
you dont have to solve the integrals, i just need to know if the way of my thinking is right or wrong. if it is wrong which path shoul i follow?
1. I think the potential will depent on only the distance from origin, there won't be any [tex]\theta[/tex] or [tex]\phi[/tex] in the equation. on the other hand, if has a charge on it not a potential, inside the shell potential would be constant. So, is it gonna be constant or not in this situation?
2. my attemp to find the potential inside shell is:
i will find the potential on P point (shown in the picture)
V(P)=k[tex]\int[/tex] [tex]\sigma[/tex] dS / r
r=(s^{2}+R^{2}2Rscos[tex]\theta[/tex])^{1/2}
dS=R^{2}sin[tex]\theta[/tex] d[tex]\theta[/tex]d[tex]\phi[/tex]
for a hemispherical shell [tex]\theta[/tex]=0pi (?) and [tex]\phi[/tex] = 02pi
if i put them in the integral and solve it the result is V(p)=2 [tex]\pi[/tex] kR [tex]\sigma[/tex] (sR)/(s)
if this is right, i can use V_{0} and find the result in terms of V_{0}. now if anyone can tell me if this is right or wrong i can continue, i will simulate this event and i really appreciate if anyone help me.
you dont have to solve the integrals, i just need to know if the way of my thinking is right or wrong. if it is wrong which path shoul i follow?
Attachments

2.9 KB Views: 542