# Two charges of  2 C  and  4 C are positioned on a line at points  -3  and  -2 , respectively. What is the net force on a charge of  3 C at  1 ?

Apr 28, 2016

$F = 15 , 38 \cdot {10}^{9} N$

#### Explanation:

${F}_{A} = k \frac{{q}_{A} \cdot {q}_{C}}{4} ^ 2$

${F}_{B} = k \frac{{q}_{B} \cdot {q}_{C}}{3} ^ 2$

$F = {F}_{A} + {F}_{B}$

$F = k \left(\frac{{q}_{A} \cdot {q}_{C}}{16} + \frac{{q}_{B} \cdot {q}_{C}}{9}\right)$

$F = 9 \cdot {10}^{9} \left(\frac{2 \cdot 3}{16} + \frac{4 \cdot 3}{9}\right)$

$F = 9 \cdot {10}^{9} \left(\frac{6}{16} + \frac{12}{9}\right)$

$F = 9 \cdot {10}^{9} \frac{\left(54 + 192\right)}{144}$

$F = 9 \cdot {10}^{9} \cdot \frac{246}{144}$

$F = 15 , 38 \cdot {10}^{9} N$