Hi everyone, I'm having trouble solving a certain equation with given boundary conditions. I'm sure its probably something obvious that I'm overlooking but I was wondering if any of you would be kind enough to offer help. I tried using integration by parts but I think I'm still going wrong somewhere.
The initial equation is:
With boundary conditions of Vz=0 on r=R and Vz=V on r=kR
So I let
Then got
and used the BC's to give
I then tried to work out C to give
(I think I might have started going wrong around here)
and inserted C into the above equations to give
.
I'm a bit stumped as to where I'm supposed to go from here. The solution is given with the question as being
Edit: The K in the solution is supposed to be small, not capital.
The only thing I can think of doing is dividing everything through by Vz to give V/Vz, which I can put on one side, but I'm pretty sure that's not what I'm supposed to be doing.
Thanks a lot to anyone who can offer advice.
The initial equation is:
With boundary conditions of Vz=0 on r=R and Vz=V on r=kR
So I let
Then got
and used the BC's to give
I then tried to work out C to give
(I think I might have started going wrong around here)
and inserted C into the above equations to give
I'm a bit stumped as to where I'm supposed to go from here. The solution is given with the question as being
Edit: The K in the solution is supposed to be small, not capital.
The only thing I can think of doing is dividing everything through by Vz to give V/Vz, which I can put on one side, but I'm pretty sure that's not what I'm supposed to be doing.
Thanks a lot to anyone who can offer advice.