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 $4.00 imes 10^{-5} N/m$, 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?

Question

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 $4.00 	imes 10^{-5} N/m$, 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?

Quizlet Admin · Accepted Answer

Consider two long, parallel wires which are separated by a distance of 2.50 cm. It is given that the force per unit length that each wire exerts on the other is $F/L=4.00 	imes 10^{-5}$ N/m. The two wires repel each others, and the
current in one wire is $I=0.600$ A.

a.

We need to find the current in the other wire. The magnitude of the force per unit length between two wires carrying currents of $I$ and $I^{\prime}$ is given by,
$$\begin{align}\frac{F}{L}=\frac{\mu_{0} I^{\prime} I}{2 \pi r}\end{align}$$
solve for $I^{\prime}$ and substitute to get,
$$\begin{align*}I^{\prime}&=\frac{F}{L} \frac{2 \pi r}{\mu_{0} I}\
&=\left(4.0 	imes 10^{-5} \mathrm{~N/m}ight) \frac{2 \pi(0.0250 \mathrm{~m})}{(4 \pi 	imes 10^{-7} \mathrm{~T \cdot m/A})(0.60 \mathrm{~A})}\
&=8.33 \mathrm{~A}\end{align*}$$

$$\boxed{I^{\prime}=8.33 \mathrm{~A}}$$

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