# What is the force, in terms of Coulomb's constant, between two electrical charges of -45 C and 60 C that are 15 m  apart?

##### 1 Answer

Force 'F' in terms of coulomb's constant 'k' is -12k Newtons.

#### Explanation:

According to the Coulomb's Law
$F = \frac{k {q}_{1} {q}_{2}}{r} ^ 2$.
Here the coulomb's constant 'k' is often written as $\frac{1}{4 \pi {\epsilon}_{\text{0}}}$ so that the force equation becomes
$F = \left[\frac{1}{4 \pi {\epsilon}_{\text{0}}}\right] \left[\frac{{q}_{1} {q}_{2}}{r} ^ 2\right]$
In S.I units , the coulomb's constant 'k' is measured to be $8.98755 \times {10}^{9} N {m}^{2} {C}^{-} 2 \approx 9 \times {10}^{9} N {m}^{2} {C}^{-} 2$
By substituting the given values in terms of 'k' we get,
Force$F = \frac{k \left(- 45\right) \left(60\right)}{15} ^ 2 = - 12 k$ Newtons.
In terms of numericals $F = - 108 \times {10}^{9}$Newtons.