A charge of 2 C is at (5, 2) and a charge of -3 C is at ( 4, -9 ). If both coordinates are in meters, what is the force between the charges?

Feb 8, 2016

${F}_{A B} \cong 0 , 4426 \cdot {10}^{9} N$

Explanation:

$\text{distance between the point A and B is given by:}$
${r}_{A B}^{2} = {\left(4 - 5\right)}^{2} + {\left(- 9 - 2\right)}^{2}$
${r}_{A B}^{2} = 1 + 121$
${r}_{A B}^{2} = 122$
$\text{force between two charge is given by Coulomb's law}$
${F}_{A B} = k \cdot \frac{- {q}_{A} \cdot {q}_{B}}{r} ^ 2$
${F}_{A B} = \frac{9 \cdot {10}^{9} \cdot 2 \cdot \left(- 3\right)}{r} ^ 2$
${F}_{A B} = \frac{- 54 \cdot {10}^{9}}{122}$
${F}_{A B} \cong 0 , 4426 \cdot {10}^{9} N$