Question

28.30 • two long, parallel wires are separated by a distance of 2.50 cm. the force per unit length that each wire exerts on the other is 4.00 × 10^{-5} n/m, and the wires repel each other. the current in one wire is 0.600 a. (a) what is the current in the second wire? (b) are the two currents in the same direction or in opposite directions?

Explanation:

Step1: Recall the formula for force per unit length

The formula for the force per unit length \(F/L\) between two parallel current - carrying wires is \(\frac{F}{L}=\frac{\mu_0I_1I_2}{2\pi r}\), where \(\mu_0 = 4\pi\times10^{-7}\ T\cdot m/A\), \(I_1\) and \(I_2\) are the currents in the two wires, and \(r\) is the separation between the wires.
We need to solve for \(I_2\). Rearranging the formula gives \(I_2=\frac{2\pi r(F/L)}{\mu_0I_1}\).

Step2: Substitute the given values

Given \(r = 2.50\ cm=0.025\ m\), \(\frac{F}{L}=4.00\times 10^{-5}\ N/m\), \(I_1 = 0.600\ A\), and \(\mu_0 = 4\pi\times10^{-7}\ T\cdot m/A\).
Substitute these values into the formula for \(I_2\):

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Step3: Determine the direction of currents

Since the wires repel each other, according to the rule: parallel currents attract and anti - parallel currents repel. So the currents are in opposite directions.

Answer:

a. The current in the second wire is \(I_2 = 8.33\ A\).
b. The two currents are in opposite directions.