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. choose the formula that represents this when solved for ( k ).
( \bigcirc ) a ( k = \frac{r^2 f}{qq} )
( \bigcirc ) b ( k = \frac{f}{r^2 qq} )
( \bigcirc ) c ( k = \frac{r^2}{f qq} )
( \bigcirc ) d ( k = \frac{qq}{r^2 f} )

Explanation:

Step1: Start with Coulomb's Law

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

Step2: Multiply both sides by \( r^2 \)

To isolate the term with \( k \), we multiply both sides of the equation by \( r^2 \). This gives us \( F\times r^2=k\times qQ \), or \( Fr^2 = kqQ \).

Step3: Divide both sides by \( qQ \)

Now, to solve for \( k \), we divide both sides of the equation \( Fr^2 = kqQ \) by \( qQ \). So we get \( k=\frac{Fr^2}{qQ} \), which can also be written as \( k = \frac{r^2F}{qQ} \).

Answer:

A. \( k=\frac{r^2F}{qQ} \)