Question

the equation $f=\frac{ki_{1}i_{2}}{2pi r}$ gives the magnetic force per unit length between two parallel wires, where $k$ is a constant, $i_{1}$ and $i_{2}$ are the currents in the two wires, and $r$ is the distance between the wires. which shows the equation solved for the distance between the wires, $r$? $r = 2pi ki_{1}i_{2}f$ $r=\frac{ki_{1}i_{2}}{f}-2pi$ $r=\frac{fki_{1}i_{2}}{2pi}$ $r=\frac{2pi f}{ki_{1}i_{2}}$ $r=\frac{ki_{1}i_{2}}{2pi f}$ $r=\frac{2pi ki_{1}i_{2}}{f}$

Explanation:

Step1: Isolate $r$

Given $F=\frac{kI_1I_2}{2\pi r}$, multiply both sides by $2\pi r$ to get $2\pi rF = kI_1I_2$.

Step2: Solve for $r$

Divide both sides of $2\pi rF = kI_1I_2$ by $2\pi F$ to obtain $r=\frac{kI_1I_2}{2\pi F}$.

Answer:

$r=\frac{kI_1I_2}{2\pi F}$ (the fifth option among the given choices)