Question

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coulombs law is given by $f = \frac{kq_1q_2}{r^2}$, where $f$ is the force, $k$ is a constant, $q_1$ and $q_2$ are the charges on the two bodies, and $r$ is the distance between them. rewrite the formula for coulombs law to solve for $r$.
the formula for $r$ is

Explanation:

Step1: Isolate \(r^{2}\)

Given \(F=\frac{Kq_{1}q_{2}}{r^{2}}\), multiply both sides by \(r^{2}\): \(Fr^{2}=Kq_{1}q_{2}\).

Step2: Solve for \(r^{2}\)

Divide both sides by \(F\): \(r^{2}=\frac{Kq_{1}q_{2}}{F}\).

Step3: Solve for \(r\)

Take the square - root of both sides. Since \(r\) represents a distance (a non - negative quantity in the context of Coulomb's law), \(r = \sqrt{\frac{Kq_{1}q_{2}}{F}}\).

Answer:

\(r=\sqrt{\frac{Kq_{1}q_{2}}{F}}\)