# Two charges of  9 C  and  -8 C are positioned on a line at points  -5  and  -1 , respectively. What is the net force on a charge of  7 C at  0 ?

Apr 3, 2016

${F}_{\text{net"=-481,32*10^9" N}}$

#### Explanation:

$\text{There are two forces acting on the object C(green)}$
$\text{These are:}$

$\text{1)"F_"AC} = k \frac{{q}_{A} \cdot {q}_{C}}{d} ^ 2$

${q}_{A} = 9 C \text{ "q_C=7C " "d=5" unit}$

${F}_{\text{AC}} = k \frac{9 \cdot 7}{5} ^ 2 = \frac{63 \cdot k}{25}$

$\text{2)"F_"BC} = k \cdot \frac{{q}_{B} \cdot {q}_{C}}{d} ^ 2$

${q}_{B} = - 8 C \text{ "q_C=7C" "d=1" unit}$

${F}_{\text{BC}} = k \cdot \frac{\left(- 8\right) \cdot 7}{1} ^ 2 = - \frac{56 \cdot k}{1}$

$\text{The net Force acting on the Object C:}$

${F}_{\text{net}} = \frac{63 \cdot k}{25} - \frac{56 \cdot k}{1}$

${F}_{\text{net}} = \frac{63 \cdot k - 1400 \cdot k}{25}$

${F}_{\text{net}} = - \frac{1337 \cdot k}{25}$

${F}_{\text{net}} = - 53 , 48 \cdot k$

$k = 9 \cdot {10}^{9} N \cdot {m}^{2} \cdot {C}^{-} 2$

${F}_{\text{net"=-481,32*10^9" N}}$