The electric force between two charges is -5uc and 12uc is 25N. Find the distance that separates them

Given that the electric force between two charges is -5 uC and 12 uC is 25 N.

We know that the formula for the electric force between two charges is given by Coulomb's Law:

F = \frac{k \cdot |q_1 \cdot q_2|}{r^2}

Where:
- F is the electric force in Newtons,
- k is Coulomb's constant, approximately 8.99 \times 10^9 N m^2/C^2,
- q_1 and q_2 are the magnitudes of the two charges in Coulombs, and
- r is the distance between the two charges in meters.

Given that the electric force is 25 N, charge q_1 = -5 \, \mu C = -5 \times 10^{-6} C and charge q_2 = 12 \, \mu C = 12 \times 10^{-6} C.

Plugging in the known values into Coulomb's Law, we get:

25 = \frac{8.99 \times 10^9 \cdot |(-5 \times 10^{-6}) \cdot (12 \times 10^{-6})|}{r^2}

Now, let's solve for r:

25 = \frac{8.99 \times 10^9 \cdot 5 \times 12 \times 10^{-12}}{r^2}

25 = \frac{8.99 \times 10^9 \cdot 60 \times 10^{-12}}{r^2}

25 = \frac{539.4 \times 10^{-3}}{r^2}

25 = \frac{539.4}{r^2}

r^2 = \frac{539.4}{25}

r^2 = 21.576

r = \sqrt{21.576}

\boxed{r \approx 4.64 \, \text{m}}

\textbf{Answer:} The distance that separates the two charges is approximately 4.64 meters.