Question

Shown at right is a cross-sectional view of two long straight wires that are parallel to one another. one wire carries a current io out of the page; the other carries an equal current io into the page. Suppose a third wire (carrying the same current io out of the page) is placed such that the magnetic field at point p has zero magnitude. e. Determine the location of the third wire. (if it helps to define a coordinate system, consider p the origin)

Answer 1

To determine the location of the third wire such that the magnetic field at point p has zero magnitude, place it equidistant between the two parallel wires along a line perpendicular to both wires.

Step-by-step explanation:

To determine the location of the third wire such that the magnetic field at point p has zero magnitude, we need to consider the magnetic field generated by the two parallel wires. The magnetic field lines around a wire carrying current flow in a circular pattern around the wire. When two parallel wires have currents flowing in opposite directions, the magnetic fields they produce cancel each other out between the wires.

Using the right-hand rule, we can determine the direction of the magnetic field at point p for each wire. Since the direction of the magnetic field should be zero at point p, the third wire should be placed equidistant between the two parallel wires, along a line perpendicular to both wires.

By placing the third wire equidistant between the two parallel wires, the magnetic field produced by the current in the third wire will cancel out the magnetic fields produced by the currents in the other wires at point p, resulting in a net magnetic field of zero.