A charge of #3 C# is at #(4 ,-7 )# and a charge of #-1 C# is at #(-2 , 4 ) #. If both coordinates are in meters, what is the force between the charges?

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Answer 1 · 2017-06-30T12:48:51

#F_e = 1.72 xx 10^8# #"N"#

We're asked to calculate the magnitude of the electric force between two point charges, for which we can use the equation

#F_e = k(|q_1q_2|)/(r^2)#

where

#k# is Coulomb's constant, equal to #8.988xx10^9("N"•"m"^2)/("C"^2)#
#q_1# and #q_2# are the two point charges (no particular order), in coulombs, #"C"#
#r# is the distance between the two charges, in meters, #"m"#

The distance between the two point charges is found using the distance formula:

#r = sqrt((4-(-2))^2 + (-7-4)^2) = color(red)(12.5# #color(red)("m"#

Plugging in our known values, we have

#F_e = (8.988xx10^9("N"•"m"^2)/("C"^2))(|(3color(white)(l)"C")(-1color(white)(l)"C")|)/((color(red)(12.5)color(white)(l)color(red)("m"))^2)#

#= color(blue)(1.72 xx 10^8# #color(blue)("N"#