A charge of 6.5 μC is placed 4.4 cm from a second charge. If the force between the charges is 5.4, what is the magnitude of the second charge in μC?

Answer 1

Since the force is just given as a number, we can't really tell if the charge in question is positive or negative (an attractive force or a repelling force). So we'll just consider the absolute value. We also are guessing the the force is given as newtons (N).

Coulomb's law is:

where k = 8.988 x 10⁹ Nm²/C²

F = 5.4 N

q₁ = 6.5 x 10^-6 C

d = 4.4/100 = 0.044 m

So:

5.4 = (8.988 x 10⁹)(6.5 x 10^-6)(q₂)/(0.044)²

Multiply both sides by 0.044² and divide both sides by 8.988 x 10⁹ and 6.5 x 10^-6 to get:

q₂ = 1.8 x 10^-7 C which can also be written as 0.18 μC or as 180 nC (nano Coulombs)

Answer 2