A charge of 5 C is at (-6, 1 ) and a charge of -3 C is at (-2, 1) . If both coordinates are in meters, what is the force between the charges?

1 Answer
Mar 20, 2016

The force between the charges is 8\times10^9 N.

Explanation:

Use Coulomb's law:
F=\frac{k\abs{q_1q_2}}{r^2}

Calculate r, the distance between the charges, using the Pythagorean theorem
r^2 = \Delta x^2 + \Delta y^2
r^2 = (-6-(-2))^2 + (1-1)^2
r^2 = (-6+2)^2 + (1-1)^2
r^2 = 4^2 + 0^2
r^2 = 16
r=4

The distance between the charges is 4m. Substitute this into Coulomb's law. Substitute in the charge strengths as well.

F=\frac{k\abs{q_1q_2}}{r^2}
F=k\frac{\abs{(5)(-3)}}{4^2}
F=k\frac{15}{16}
F = 8.99×10^9(\frac{15}{16}) (Substitute in the value of Coulomb's constant)
F=8.4281\times 10^9 N
F=8 \times 10^9 N (As you're working with one significant figure)