# Two charges of  -6 C  and  4 C are positioned on a line at points  -6  and  9 , respectively. What is the net force on a charge of  -1 C at  1 ?

Jan 20, 2016

$1.16 \times {10}^{9} \text{N}$ to the right

#### Explanation:

You have to use the superposition principle. The net force is the vector sum of all the external forces acting on the -1C charge.

To calculate the electrical attractive/repulsive forces, we use Coulomb's Law. Coulomb's Law states that the electrostatic force is directly proportional to the charge of each object and has an inverse-squared relationship with the distance between the 2 charges.

Mathematically,

${F}_{\text{e}} = \frac{k {Q}_{1} {Q}_{2}}{{r}_{12}^{2}}$

$k \approx 9 \times {10}^{9} {\text{Nm"^2"C}}^{- 2}$ is the constant of proportionality,
a.k.a. Coulomb's constant.

${Q}_{1}$ and ${Q}_{2}$ are the charge of the 2 charges respectively.

${r}_{12}$ is the distance between the 2 charges.

From the formula, we can see that whether the force is attractive or repulsive depends on whether we are dealing with unlike charges or like charges.

In this question, I assume that the distance is measured in meters, since it is not specified.

The force exerted by the -6C at -6 is given by the coulomb law,

F_1 = frac{k(-6"C")(-1"C")}{(7"m")^2}~~1.10xx10^9 "N"

Since the unlike charges repel, the force is directed towards the right.

The force exerted by the 4C at 9 is given by the coulomb law,

F_2= frac{k(4"C")(-1"C")}{(8"m")^2}~~-6.25xx10^7 "N"

Since the like charges attract, the force is directed towards the right.

I recommend you to draw a diagram of the 3 charges to visualize it more clearly.

The sum of the 2 forces is $1.16 \times {10}^{9} \text{N}$ to the right.