Solve for k F=k(qQ)/(r^2)

$F = k \frac{q Q}{r^{2}}$

Step 1

Rewrite the equation as $k (\frac{q Q}{r^{2}}) = F$ .

$k (\frac{q Q}{r^{2}}) = F$

Step 2

Simplify.

Combine $k$ and $\frac{q Q}{r^{2}}$ .

$\frac{k (q Q)}{r^{2}} = F$

Remove parentheses.

$\frac{k q Q}{r^{2}} = F$

Step 3

Multiply each term in $\frac{k q Q}{r^{2}} = F$ by $\frac{r^{2}}{q Q}$ to eliminate the fractions.

Multiply each term in $\frac{k q Q}{r^{2}} = F$ by $\frac{r^{2}}{q Q}$ .

$\frac{k q Q}{r^{2}} \cdot \frac{r^{2}}{q Q} = F \frac{r^{2}}{q Q}$

Simplify the left side.

Combine.

$\frac{k q Q r^{2}}{r^{2} (q Q)} = F \frac{r^{2}}{q Q}$

Cancel the common factor of $q$ .

Cancel the common factor.

$\frac{k q Q r^{2}}{r^{2} (q Q)} = F \frac{r^{2}}{q Q}$

Rewrite the expression.

$\frac{k Q r^{2}}{r^{2} (Q)} = F \frac{r^{2}}{q Q}$

Cancel the common factor of $Q$ .

Cancel the common factor.

$\frac{k Q r^{2}}{r^{2} Q} = F \frac{r^{2}}{q Q}$

Rewrite the expression.

$\frac{k r^{2}}{r^{2}} = F \frac{r^{2}}{q Q}$

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{k r^{2}}{r^{2}} = F \frac{r^{2}}{q Q}$

Divide $k$ by $1$ .

$k = F \frac{r^{2}}{q Q}$

Simplify the right side.

Combine $F$ and $\frac{r^{2}}{q Q}$ .

$k = \frac{F r^{2}}{q Q}$