Boundary Conditions Laplace

Hi there, im solving laplace equation in a code i made in C. Im using Finite Difference Method in order to simulate the current pattern. I used the stream function to do that.

Electrode
0.--0--0--0--0--0--0--0-==========-1--1--1--1--1--1--1--1 1
0. 1
(Plasma Flow) --------> 　　 xxxxxxx (x =B Magnetic Field)
0. 　　xxxxxxx 1
0. 1
--0--0--0--0--0--0--0--==========-1--1--1--1--1--1--1--1 1
Electrode

The problem is very simplificated of course. My boundary conditions are the ones showed in the schecth. So my function U goes from 0 to 1, and in the electrodes i put a function so U can be satisfied; and inside the channel, the classic equation of finite difference. I can obtain the current patern but my quention is: How can i introduce the effect of the magnetic field inside the channel?. I was thinking in introducing some Neumann conditions in those points, so the gradient of the funtions varies in order to "simulate" the force of the magnetic field.