A charge of #5# # C# is at #(9, 3)# and a charge of #-2# # C# is at #(-2, 7) #. If both coordinates are in meters, what is the force between the charges?

1 Answer
Mar 5, 2016

Answer:

The force between two charges is given by Coulomb's Law: #F=(kq_1q_2)/r^2#. Calculating the distance to be #11.7# #m# and knowing #k=9.0xx10^9# #Nm^2C^-2#, we find #F=9.85xx10^8# #N#

Explanation:

The distance formula for the distance between two points in (2 dimensional) space is:

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#=sqrt((-2-9)^2+(7-3)^2)=sqrt137~~11.7# #m#

Using Coulomb's Law we find:

#F=(kq_1q_2)/r^2=(k*5*-3)/11.7^2=(-15k)/137# #N#.

This is the answer in terms of #k#, but we can substitute in the value of the constant to give the final answer in #N#, as shown above.