# Two charges of  -3 C  and  2 C are positioned on a line at points  6  and  4 , respectively. What is the net force on a charge of  3 C at  2 ?

Feb 17, 2016

${F}_{N} \cong 8 , 44 \cdot {10}^{9} N$

#### Explanation:

$\text{distance between 2C and 3C is :} 4 - 2 = 2$
$\text{distance between -3C and 3C is :} 6 - 2 = 4$
$\text{Force between two charges is given by :} F = \frac{k \cdot {q}_{1} \cdot {q}_{2}}{d} ^ 2$
$\text{Force between 2C and 3C :} {F}_{2 C \leftarrow 3 C} = \frac{k \cdot 2 \cdot 3}{2} ^ 2 = \frac{3 \cdot k}{2}$
$\text{Force between -3C and 3C :} {F}_{- 3 C \rightarrow 3 C} = \frac{k \cdot 3 \cdot \left(- 3\right)}{4} ^ 2$
${F}_{- 3 C \rightarrow 3 C} = \frac{- 9 \cdot k}{16}$
$\text{Net Force on the charge of 3C :} {F}_{2 C \leftarrow 3 C} + {F}_{- 3 C \rightarrow 3 C}$
${F}_{N} = \frac{3 \cdot k}{2} - \frac{9 \cdot k}{16}$
${F}_{N} = \frac{24 \cdot k - 9 \cdot k}{16}$
${F}_{N} = \frac{15 \cdot k}{16}$
${F}_{N} = \frac{15 \cdot 9 \cdot {10}^{9}}{16}$
${F}_{N} \cong 8 , 44 \cdot {10}^{9} N$