-1
$\begingroup$

I want to calculate (with Poisson's equation) the electric field in the region containing a point charge near an infinite conducting plane with 0 potential. My textbook uses V(x,y,z)= 0 for every x,y,x of the plane as boundary condition.

However, in resolving Poisson's equation don't we need to use the boundary condition of a surface that encloses the portion of space we are studying? In this case the infinite plane is not a closed surface. Where am i wrong?

$\endgroup$
1
$\begingroup$

The other boundary condition is that the potential goes to zero at infinity.

$\endgroup$
  • $\begingroup$ What are the rules for defining the correct boundary conditions ? I searched by there is nothing clear on the web.... $\endgroup$ – JDOE Nov 18 '17 at 8:43
  • 1
    $\begingroup$ Whenever the charge distribution is localized, the potential at infinity goes to zero. (Or to any constant, if you feel like defining it to be non-zero). $\endgroup$ – Chris Nov 18 '17 at 9:47
  • $\begingroup$ @JDOE, since the conducting plane (an equipotential surface) extends to infinity and is at zero potential, what other reasonable choice for the potential at infinity is there? $\endgroup$ – Alfred Centauri Nov 18 '17 at 13:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.