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 $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$. Given $I_1 = 12 \, \text{A}$, $I_2 = 14 \, \text{A}$, and $r = 0.42 \, \text{m}$, and considering a length $L = 6.4 \, \text{m}$ of one of the wires, the force can be calculated as follows: $F = L \times \frac{\mu_0 I_1 I_2}{2\pi r}$. Substituting the given values and solving gives a force of approximately $5.1 \times 10^{-4} \, \text{N}$.

A Very Long Straight Wire Carries a 12-A Current Eastward