Question

coulombs law ( f = k \frac { q q } { 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 ).
a. ( k = \frac { r ^ { 2 } f } { q q } )
b. ( k = \frac { f } { r ^ { 2 } q q } )
c. ( k = \frac { r ^ { 2 } } { f q q } )
d. ( k = \frac { q q } { r ^ { 2 } f } )

Explanation:

Step1: Multiply both sides by \(r^{2}\)

Given \(F = k\frac{qQ}{r^{2}}\), multiply both sides by \(r^{2}\):
\(F\times r^{2}=k\frac{qQ}{r^{2}}\times r^{2}\)
\(r^{2}F = kqQ\)

Step2: Divide both sides by \(qQ\)

Divide \(r^{2}F = kqQ\) by \(qQ\):
\(\frac{r^{2}F}{qQ}=\frac{kqQ}{qQ}\)
\(k=\frac{r^{2}F}{qQ}\)

Answer:

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