Current, B, E field directions on line in TEM mode

[yabb dabba do]

Hi,

Say you have a two conductor transmission line in TEM mode. The E and B field's will look something like the picture below with the E field in blue and the B field in red.

The E field should point in the direction of the current, as it's what makes the charges move. The E field in the picture below is orthogonal to the two conductors, indicating the charges and thus the current would move in a direction orthogonal to the conductors axis.

However ampere's law says that the B field is created in circles around the direction of the current. The B field circles below are around the axis of the conductors, indicating that the current should be traveling axially along the conductors.

So I'm confused. In a two conductor transmission line in TEM mode the E field indicates the charges should be moving in an orthogonal direction to the conductors, but the B field indicates the charges should be moving axially along the conductors. :

 

[Baluncore]

So I'm confused. In a two conductor transmission line in TEM mode the E field indicates the charges should be moving in an orthogonal direction to the conductors,

The differential voltage between the two conductors and the electron conduction wave propagate along the line as the capacitance of the line is charged through the inductance of the line. Electrons cannot escape the surface of the line so they have to go down the line until they reach a resistive load or are reflected by a mismatch. The E field appearing between the two wires is the difference in the voltage across the capacitance of the line as it is charged by the inductively limited currents in the two wires.