PS - I tried to put this question on the physics stackexchange, but the over-vigilant moderators closed the thread for a reason I can't comprehend. This forum is much nicer! :)
Hi Andy, thanks for your suggestion. However this is a problem which is independent of the z-dimension, so no special functions should be needed. I'll state the problem again and perhaps someone may have another idea: an electric field is applied at infinity...
Hi Vanhees71, thanks again for looking into this. Yes I figured the previous solution was incorrect...as you said the boundary and interface conditions aren't satisfied. Perhaps the ansatz you proposed may lead somewhere - I will look at this next. If it doesn't lead somewhere I may just make a...
Thank you very much for this nice analysis - this has been bugging me for some time. The solution you obtained; is this field not discontinuous in the limit when approaching ##v\rightarrow1/(2c)## from either side?
Before I considered the parabola, I considered the an elliptical inclusion of...
Hi vanhees71, thanks for your reply. I can't figure out how shifting the parabola to the right (to get the focus coincident with the origin) in Cartesian coordinates before working in parabolic coordinates will help? Surely the potential field will just be scaled by a constant?
The problem is...
Thanks for the advice. I was hoping there'd be a simpler solution (all terms with n>1 vanish) like that for the case of an elliptical inclusion of a different conductivity.
I stumbled across this: http://eqworld.ipmnet.ru/en/solutions/lpde/lpde301.pdf
They list one of the particular solutions in...
I'm stuck on a seemingly simple 2D electrostatics problem. The problem is as follows:
A parabolic interface ($$x(y)=cy^2$$) separates two regions of different conductivities, with a uniform electric field at infinity aligned with the x-axis.
I write the Laplace operator in parabolic...
Hi - wondering if you can help me find a solution of:
\nabla^{2}u-\frac{u}{\lambda^{2}}=a\delta(r)
for spherical symmetry in 3D with the condition that \lim_{r\rightarrow \infty}u=0. It can be rewritten in spherical coordinates as
\frac{1}{r^{2}}\frac{\partial}{\partial...