A charge of #-2 C# is at #(-2 , 1 )# and a charge of #-1 C# is at #(5, 3) #. If both coordinates are in meters, what is the force between the charges?

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Answer 1 · 2017-01-27T21:17:40

According to Coulumbs Law: #mathbf F = (k Q_1Q_2)/(abs(\mathbf r_1 - \mathbf r_2)^2) mathbf e_(r_1 - r_2)#

Coulumb's Constant is #k approx 8.99×10^9 Nm^2#/#C^2#

The magnitude of the force evaluates as:

#| mathbf F |= ( 8.99×10^9 * (-2) * (-1))/(abs(((5),(3)) - ((3),(1)))^2) = 2.2475 * 10^9 N#

....with #abs(\mathbf r_1 - \mathbf r_2)^2 = 8#.

[The answer may look big but note that a charge of "only" 1C is a lot of charge.]