Question

two parallel wires separated by 2.00 cm each carry 21.0 a and experience a force of 0.800 n. if one wire is very long, how long is the other one?

Explanation:

Step1: Recall the formula for force between two parallel current - carrying wires

The formula for the force per unit length between two parallel current - carrying wires is $F/L=\frac{\mu_0I_1I_2}{2\pi r}$, where $\mu_0 = 4\pi\times10^{- 7}\ T\cdot m/A$, $I_1$ and $I_2$ are the currents in the wires, and $r$ is the distance between the wires. We want to find the length $L$ of the non - very long wire. We can re - arrange the formula for the total force $F$ (since $F=(F/L)L$) to $L=\frac{F\times2\pi r}{\mu_0I_1I_2}$.

Step2: Identify the given values

We are given that $I_1 = I_2=21.0\ A$, $r = 2.00\ cm=0.02\ m$, $F = 0.800\ N$, and $\mu_0 = 4\pi\times10^{-7}\ T\cdot m/A$.

Step3: Substitute the values into the formula

Substitute the values into $L=\frac{F\times2\pi r}{\mu_0I_1I_2}$.

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Answer:

$181\ m$