# Magnetic field between two current-carrying wires

Two wires of infinite length are placed at a distance D = 10cm on opposite sides of a point O, both wires carry the same current of 1.0 A, in which direction must this current flow in order for the magnetic field strength at O to be non-zero.

Consider a general point on the line joining the 2 wires and a distance d away from the mid point O.

By summing the magnetic field due to currents of magnitude i flowing in both wires in the sense you found in (a), show that, on the line joining the two wires, the magnetic field strength is given by (see attachment for expression)

An electron is traveling at 5.0 x 106 m s-1 directly into the page at the point P shown in figure 1. P is 4.0 cm from O. Again D = 10 cm and the currents i in both wires have magnitudes of 1.0 A and are flowing in the directions given and found in question (a). find the magnitude and direction of the force that the electron experiences.

See attached file for full problem description.

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#### Solution Summary

The solution discusses the magnetic field induced by two infinitely long wires by employing Ampere's law. It also shows how to calculate the magnetic force on a moving charge.