let's consider a system made with 3 conductors: two parallel wires (in this case rectangular wires) and a plane (GND) below them. Consider the following situation in which both wires are connected to the same potential (with respect to GND). This situation is called "even mode" and results in this field configuration:
How can I deduce those field lines of E and H? Do you know a criterion to find their distribution in space?
I think that E goes between points with different potentials. Since the two wires have the same potentials, lines start from each wires and go towards GND but not towards the other wire. Is it correct?
For the magnetic field, I would say it is equal to 0 at the centre of the space between the two wires, why is it not 0 in the picture?