Force on parallel wires: A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward. The wires are parallel to each other and are 42 cm apart. Calculate the force on a 6.4 m length of one of the wires. (μ₀ = 4π × 10^-7 T ∙ m/A)

Question

Quizplus · Accepted Answer

The force per unit length between two parallel currents $I_1$ and $I_2$, separated by a distance $r$, is given by the formula $F/L = \frac{\mu_0 I_1 I_2}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$. Substituting the given values ($I_1 = 12 \, \text{A}$, $I_2 = 14 \, \text{A}$, $r = 0.42 \, \text{m}$, and $L = 6.4 \, \text{m}$), we can calculate the force on the 6.4 m length of one of the wires. The currents are in opposite directions, which means they attract each other. The calculation yields a force of $5.1 \times 10^{-4} \, \text{N}$, which corresponds to choice B.

Force on Parallel Wires: a Very Long Straight Wire Carries