A charge of #-2 C# is at #(-2 , 1 )# and a charge of #-1 C# is at #(1 ,-3) #. If both coordinates are in meters, what is the force between the charges?

1 Answer
Jan 14, 2016

Answer:

The force between the charges is given by Coulomb's Law, #F = (kq_1q_2)/r^2# , and when the distance is correctly calculated is found to be #1.08*10^9 N#.

Explanation:

The first step is to find the distance between the two charges:

#d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#d = sqrt((1-(-2))^2+((-3)-1)^2)#
#d = sqrt(3^2+(-4)^2) = sqrt(25) = 5#

So the points are #5 m# apart.

Now use Coloumb's Law. The constant k has the value #9*10^9 (Nm^2)C^-2#.

#F = (kq_1q_2)/r^2# = #(9*10^9*-2*-1)/5^2# = #(2.7*10^10)/25#

#F = 1.08*10^9 N#

This is quite a large force, but it's unsurprising because a coulomb is quite a large amount of electric charge, and because the constant in Coulumb's Law is so large (electrostatic forces are much stronger than gravitational forces, for example).