Final answer:
The magnitude of the force per unit length on wire A can be calculated using the magnetic force formula for current-carrying wires, applying the right-hand rule for direction, and expressing the final result in N/m.
Step-by-step explanation:
To find the magnitude of the force per unit length on wire A, we use the provided information about the current in the wires and their positions.
If the currents are flowing out of the page and wire A is at (0.0 cm, 3.0 cm) while wire B is at (4.0 cm, 0.0 cm), we can calculate the magnetic force exerted by one wire onto the other by applying the formula for the magnetic force between two current-carrying wires.
The force per unit length ℒ can be calculated using the formula ℒ = I1I2µ0/2πr, where I1 and I2 are the currents in the two wires, µ0 is the permeability of free space, and r is the distance between the wires.
The final step is to calculate the direction of the force using the right-hand rule and vector addition if necessary. The resulting force per unit length on wire A can be expressed in newtons per meter (N/m).