Resultant magnetic field at centre of current carrying conductors is shown in figure. Currents are flowing in anti-parallel direction
Magnetic field direction at centre can be realised using right hand rule. It can be seen that magnetic field due to
both current carrying conductor are added together and in same direction at mid point between conductors.
As per the current direction in both wire, direction of magnetic field is perpendicular to the plane of figure and pointing inward direction.
If the charge at mid point of both wires has velocity in the direction perpendicular to plan of figure,
then velocity of charge is parallel to direction of magnetic field. Hence force acting on the charge is zero