Two parallel wires separated by 3.75 cm repel each other with a force per unit length of 1.5 x 10-4 N/m. The current in one wire is 5 A.Find the current in the other wire.
Question
Two parallel wires separated by 3.75 cm repel each other with a force per unit length of 1.5 x 10-4 N/m. The current in one wire is 5 A.Find the current in the other wire.
Solution
The force between two parallel wires carrying current is given by Ampere's force law:
F/L = μ0 * I1 * I2 / (2πr)
where: F/L is the force per unit length, μ0 is the permeability of free space (4π x 10^-7 T m/A), I1 and I2 are the currents in the two wires, r is the distance between the wires.
We are given: F/L = 1.5 x 10^-4 N/m, μ0 = 4π x 10^-7 T m/A, I1 = 5 A, r = 3.75 cm = 0.0375 m.
We need to find I2.
Rearranging the formula for I2, we get:
I2 = F * 2πr / (μ0 * I1)
Substituting the given values, we get:
I2 = (1.5 x 10^-4 N/m) * 2π * 0.0375 m / (4π x 10^-7 T m/A * 5 A)
Solving this, we get:
I2 = 0.45 A.
So, the current in the other wire is 0.45 A.
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