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?

1 Answer
Nov 19, 2016

Answer:

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