Question

Two parallel wires. Consider two infinitely long parallel wires, each carrying a steady current of I in the z direction, one passing through the point (2,0,0) and the other through (0,2,0). Find B at the origin.

Answer 1

The magnetic field at the origin due to the parallel wires can be found using the Biot-Savart law and the right-hand rule. The magnetic field produced by each wire will be in the same direction and will add up at the origin. The magnetic field at the origin is twice the magnetic field produced by one wire.

Step-by-step explanation:

The magnetic field at the origin due to the two parallel wires can be found using the Biot-Savart law. The Biot-Savart law states that the magnetic field at a point in space due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

In this case, the two wires are parallel and in the z-direction. The magnetic field produced by each wire will be in the same direction and can be determined using the right-hand rule. The magnetic fields from both wires will add up at the origin.

Since the wires are infinitely long, the distance between the origin (0,0,0) and any point on the wires is the same. Therefore, the magnetic field at the origin due to the parallel wires will be twice the magnetic field produced by one wire.