Final answer:
The force between two parallel wires carrying currents can be calculated using the magnetic constant, the currents in the wires, the length of the wires, and the distance between them. The direction of the force is determined by the right-hand rule and can either be attractive or repulsive. This force has practical implications for the structural integrity and safety of electrical systems like light-rail commuter trains.
Step-by-step explanation:
Magnitude and Direction of Force Between Wires
The question you're asking is related to the concept of electromagnetic forces. Given that we have two parallel wires carrying electric current, they will indeed exert a force on each other. This is explained by Ampère's Law and the Biot-Savart Law, which are part of the fundamentals of electromagnetic theory.
To calculate the force, we use the formula for the force between two parallel currents:
F = µ₀ * I1 * I2 * l / (2 * π * r), where:
µ₀ is the magnetic constant (4π x 10^-7 T·m/A),
I1 and I2 are the currents in the wires (800 A in this case),
l is the length of the wire (50.0 m), and
r is the distance between the wires (0.75 m).
The direction of the force can be determined by the right-hand rule. If the currents run in the same direction, the force will be attractive, causing the wires to pull towards each other. If the currents are opposite, the force will be repulsive, pushing the wires apart.
Practical Consequences
In practical situations, such a force could cause the wires to move, leading to potential disconnections or physical strain. Over long distances and with high currents, these forces can be significant, potentially requiring additional support structures or spacing considerations to ensure safe and continuous operation of the commuter train system.