Question

A charge of `-2 C` is at `(6 , -5 )` and a charge of `-4 C` is at `(-3 , -9 )`. If both coordinates are in meters, what is the force between the charges?

Answer 1

The force between the charges is `0.74xx10^9` Newtons.

Explanation:

According to the Coulomb's Law, the magnitude of the electric force exerted by a charge '`q_1`' on another charge '`q_2`' a distance '`r`' away is thus, given by
`F_e=(k|q_1q_2|)/r^2`
Here the value of '`k`' in SI units is
`k= 8.987551787xx10^9 (N-m^2)/C^2`
`k~~8.988xx10^9(N-m^2)/C^2`
Using the given coordinates we can find of the distance between them:
Distance`r=sqrt[(x_2-x_1)^2+(y_2-y_1)^2]`
Calculating with given values we get ,
`r=sqrt(97)=9.84 m`

Substituting all given values in above force equation we get,
`F_e={8.988xx10^9(N-m^2)/C^2}{[(-2C)(-4C)]/[sqrt(97)m]^2}`
`:. F= 0.74xx10^9` Newtons