Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in opposite directions. The force per unit length in N/m of one wire on the other is: A) 1 *10^-³, repulsive B) 1 *10^-³, attractive C) 4 * 10^-⁵, repulsive D) 4 *10^-⁵, attractive E) none of these

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Quizplus · Accepted Answer

The force per unit length between two parallel wires carrying current is given by: $$F=\frac{\mu_0}{2\pi}\frac{I_1 I_2}{d}$$ where $\mu_0$ is the permeability of free space, $I_1$ and $I_2$ are the currents in the wires, and $d$ is the distance between the wires. Substituting the given values, we have: $$F=\frac{\mu_0}{2\pi}\frac{(2 ext{ A})(4 ext{ A})}{0.04 ext{ m}}$$ $$F=\frac{\mu_0}{\pi}\frac{(2 ext{ A})(4 ext{ A})}{4 ext{ cm}}$$ Using the value of $\mu_0$, we get: $$F=2 imes10^{-7} imes\frac{(2 ext{ A})(4 ext{ A})}{4 ext{ cm}}$$ Simplifying, we get: $$F=4 imes10^{-6} ext{ N/m}$$ The currents are in opposite directions, so the forces are repulsive. Therefore, the answer is (C) 4 F1F1F1S1F1F1F10 10^-⁵, repulsive.

Two Parallel Wires, 4 Cm Apart, Carry Currents of 2