12.2 Magnetic Field Due to a Thin Straight Wire

Using the example, keeping the currents the same in wires 1 and 3, what should the current be in wire 2 to counteract the magnetic fields from wires 1 and 3 so that there is no net magnetic field at point P?

How would you orient two long, straight, current-carrying wires so that there is no net magnetic force between them? (Hint: What orientation would lead to one wire not experiencing a magnetic field from the other?)

The magnitude of the magnetic field 50 cm from a long, thin, straight wire is $8.0 \mu\text{T} .$ What is the current through the long wire?

A long, straight, horizontal wire carries a left-to-right current of 20 A. If the wire is placed in a uniform magnetic field of magnitude $4.0 \times 10^{−\text{5}} \text{T}$ that is directed vertically downward, what is the resultant magnitude of the magnetic field 20 cm above the wire? 20 cm below the wire?

Consider the area between the wires of the preceding problem. At what distance from the top wire is the net magnetic field a minimum? Assume that the currents are equal and flow in opposite directions.