Final answer:
Magnetic forces between two parallel wires depend on their currents' directions. To find the current in the second wire, the magnetic force law is used, but additional force data is needed. Electrical systems must account for such forces in their design for safety and functionality.
Step-by-step explanation:
Current in Parallel Wires and Magnetic Forces
If two parallel wires are separated by a certain distance and carry electric currents, they exert magnetic forces on each other according to Ampère’s force law. Whether the force is attractive or repulsive depends on the direction of the currents: if currents are in the same direction, the force is attractive, and if the currents are in opposite directions, the force is repulsive.
In your case, two wires repel each other indicating that the currents flow in opposite directions. To find the current in the second wire, you would apply the formula for the magnetic force per unit length between two parallel currents, which is given by:
F/L = (μ0/2π) * (I1 * I2 / d)
where F is the magnetic force, L is the length of the wires, μ0 is the magnetic constant (4π x 10⁻⁷ T*m/A), I1 and I2 are the currents in the first and second wire, respectively, and d is the separation between the wires. To solve for the unknown current, information about the force experienced or produced by the wires is necessary. Without this information, the exact value of the current in the second wire cannot be determined from the given details.
Real-world applications such as electric train systems and household appliance cords must consider these magnetic forces. For example, electric trains use heavily insulated thick wires to handle the significant magnetic forces produced by the high currents needed for operation. Appliance cords are designed with the wires close together to minimize these forces and still manage safety and flexibility.