A charge of #2 C# is at #(-3,7)# and a charge of #-1 C# is at #( 2, -9 )#. If both coordinates are in meters, what is the force between the charges?

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Answer 1 · 2016-10-05T20:29:43

#F ~~ -6.40×10^7 N# where negative indicates an attractive force.

Let's look up Coulomb's Law and its associated constant:

#F = k_e(q_1q_2)/(r²)#

Where #k_e = 8.99×10^9 Nm²C^-2#

We use the given points to compute the square of the distance between the charges:

#r² = (2 - -3)² + (-9 - 7)²#

#r² = (5)² + (-16)²#

#r² = 25 + 256#

#r² = 281 m^2#

#F = ((8.99×10^9 Nm²C^-2)(2 C)(-1 C))/(281 m^2)#

#F ~~ -6.40×10^7 N#