To determine the magnitude of the electrical force between two point charges, we will use Coulomb's Law, which states that the force (F) between two point charges is directly proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The law is mathematically expressed as:
\[ F = k \frac{|q1 \cdot q2|}{r^2} \]
where:
F is the force between the charges,
q1 and q2 are the charges (in Coulombs, C),
r is the distance between the charges (in meters, m),
k is Coulomb's constant (\(8.9875 \times 10^9 N \cdot m^2/C^2\)).
Given in the problem are the charges and the distance:
\( q1 = 8 \times 10^5 C \)
\( q2 = 8 \times 10^5 C \)
\( r = 16 m \)
Now we use Coulomb's Law to find the magnitude of the force:
\[ F = \left( 8.9875 \times 10^9 \frac{N \cdot m^2}{C^2} \right) \frac{|8 \times 10^5 C \cdot 8 \times 10^5 C|}{(16 m)^2} \]
First, let's calculate the denominator (16 m)^2:
\( (16 m)^2 = 256 m^2 \)
Now plug this into the formula and calculate F:
\[ F = \left( 8.9875 \times 10^9 \frac{N \cdot m^2}{C^2} \right) \frac{|64 \times 10^{10} C^2|}{256 m^2} \]
\[ F = \left( 8.9875 \times 10^9 \frac{N \cdot m^2}{C^2} \right) \left( 2.5 \times 10^{8} \frac{C^2}{m^2} \right) \]
\[ F = 2.246875 \times 10^{18} N \]
So the magnitude of the force is approximately \( 2.246875 \times 10^{18} \) Newtons.
Regarding whether the charges are repelling or attracting, since both point charges have the same sign (both are positive), according to the principle of electrostatics, like charges repel each other. Therefore, the charges are repelling.
