Final answer:
The magnetic field experienced by one of the wires due to the other three, all carrying the same current, can be calculated using the Biot-Savart law. The combined magnetic fields from the two nearest neighboring wires contribute to the field at the wire in question, with their effects added together. The direction of the field follows the right-hand rule.
Step-by-step explanation:
Calculating the Magnetic Field Due to Three Wires
The student asks about the magnetic field experienced by one of the four wires due to the other three, which are all carrying the same current in the same direction.
To calculate the magnetic field at one wire due to the others in the arrangement given (a square with sides of 4.0 cm), we use the Biot-Savart law or Ampere's law.
The magnetic field due to a long straight wire at a distance 'r' is given by B = (µ0I)/(2πr), where I is the current and µ0 is the permeability of free space. For each neighboring wire, the distance 'r' will be 4.0 cm.
The fourth wire will not contribute to the field at the wire in question because it is symmetrical to one of the wires, effectively canceling out its magnetic influence at that position.
Calculation for one wire will be: B = (µ0×2.0A)/(2π×0.04m). Since there are two wires at the same distance contributing to the field, we multiply this by 2 to find the combined field.
The direction of the exerted magnetic field will follow the right-hand rule, curving around the wire in a direction determined by the current flow. Since the currents are parallel and in the same direction, the force between any two wires will be attractive.