# What is the force, in terms of Coulomb's constant, between two electrical charges of 16 C and -2 C that are 9 m  apart?

May 1, 2018

$\implies F = 3.55 \times {10}^{9} \text{ N}$

or

$\implies F = 0.395 k \text{ N}$

#### Explanation:

Coulomb's Law states that the force between two charges ${q}_{1}$ and ${q}_{2}$ separated by distance $r$ is:

$\implies F = k \frac{| {q}_{1} | | {q}_{2} |}{r} ^ 2$

where k = 8.99 xx 10^9 ("N" * "m") / "C"^2

Hence,

$F = \left(8.99 \times {10}^{9}\right) \frac{| 16 | | - 2 |}{9} ^ 2$

$F = \left(8.99 \times {10}^{9}\right) \left(0.39506\right)$

$\implies F = 3.55 \times {10}^{9} \text{ N}$

If you do want this only in terms of the constant, then this problem is simpler.

$\implies F = 0.395 k$