g1=2*10^-9 кл g2=4*10^-9кл k=9*10^9H*m2/kl2 F=80*10^-3H r-?
To find the distance \( r \) between the two charges \( g_1 \) and \( g_2 \), we can use Coulomb's Law, which states that the force \( F \) between two point charges is given by the formula:
\[ F = k \cdot \frac{|g_1 \cdot g_2|}{r^2} \]
Where:
- \( F \) is the force between the charges (given as \( 80 \times 10^{-3} \) N),
- \( k \) is Coulomb's constant (given as \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( g_1 \) and \( g_2 \) are the charges (given as \( g_1 = 2 \times 10^{-9} \, \text{C} \) and \( g_2 = 4 \times 10^{-9} \, \text{C} \)),
- \( r \) is the distance between the charges (which we need to find).
Rearranging Coulomb's law to solve for \( r \):
\[ r = \sqrt{k \cdot \frac{|g_1 \cdot g_2|}{F}} \]
Substituting the known values into the formula:
\[ r = \sqrt{9 \times 10^9 \cdot \frac{|(2 \times 10^{-9}) \cdot (4 \times 10^{-9})|}{80 \times 10^{-3}}} \]
Calculating \( |(g_1 \cdot g_2)| \):
\[ |g_1 \cdot g_2| = |(2 \times 10^{-9}) \cdot (4 \times 10^{-9})| = 8 \times 10^{-18} \, \text{C}^2 \]
Now substituting this back into the equation for \( r \):
\[ r = \sqrt{9 \times 10^9 \cdot \frac{8 \times 10^{-18}}{80 \times 10^{-3}}} \]
Calculating the fraction:
\[ \frac{8 \times 10^{-18}}{80 \times 10^{-3}} = \frac{8}{80} \times 10^{-15} = 0.1 \times 10^{-15} = 1 \times 10^{-16} \]
Now substituting this back into our equation for \( r \):
\[ r = \sqrt{9 \times 10^9 \cdot 1 \times 10^{-16}} = \sqrt{9 \times 10^{-7}} = 3 \times 10^{-4} \, \text{m} \]
Thus, the distance \( r \) between the two charges is:
\[ r = 3 \times 10^{-4} \, \text{m} \quad \text{or} \quad 0.3 \, \text{mm} \]
