Question

coulomb’s law, ( f = k \frac{qq}{r^2} ), relates the force ( f ) between two charges ( q ) and ( q ), which are a distance of ( r ) units apart. solve the formula for ( k ).

a. ( k = \frac{qq}{fr^2} )

b. ( k = \frac{fr}{qr^2} )

c. ( k = \frac{sqrt{fr}}{qq} )

d. ( k = \frac{fr^2}{qq} )

Explanation:

Step1: Start with Coulomb's Law formula

We have the formula \( F = k\frac{qQ}{r^2} \). Our goal is to solve for \( k \).

Step2: Isolate \( k \) by multiplying both sides by \( \frac{r^2}{qQ} \)

To isolate \( k \), we can multiply both sides of the equation by \( \frac{r^2}{qQ} \).
\[
F\times\frac{r^2}{qQ}=k\frac{qQ}{r^2}\times\frac{r^2}{qQ}
\]
Simplifying the right - hand side, the \( qQ \) and \( r^2 \) terms cancel out, leaving us with \( k \). On the left - hand side, we have \( \frac{Fr^2}{qQ} \). So \( k=\frac{Fr^2}{qQ} \).

Answer:

D. \( k = \frac{Fr^{2}}{qQ} \)