(a) Two point charges totaling 8.50 µC exert a repulsive force of 0.100 N on one another when separated by 0.839 m. What is the charge on each?
smallest charge (µC)
largest charge (µC)
(b) What is the charge on each if the force is attractive?
smallest charge (µC)
largest charge (µC)
IDK I WANT ANSWERS MYSELF
To solve this problem, we can use Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
(a) In this case, we are given the force (0.100 N) and the distance between the charges (0.839 m). We need to find the charge on each.
Let's denote the charges as q1 and q2. Since both charges are the same in magnitude and repulsive, we can write:
F = k * (q1 * q2) / r^2
where F is the force, k is Coulomb's constant (8.99 x 10^9 N·m^2/C^2), r is the distance between the charges, and q1 and q2 are the charges on the charges.
We know that the total charge is 8.50 µC, so we can write:
q1 + q2 = 8.50 µC
Now, let's substitute the given values into the equation:
0.100 N = (8.99 x 10^9 N·m^2/C^2) * ((q1 * q2) / (0.839 m)^2)
Simplifying this equation, we can find the product of the charges:
(q1 * q2) = (0.100 N * (0.839 m)^2) / (8.99 x 10^9 N·m^2/C^2)
(q1 * q2) = 7.47 x 10^-11 C^2
Now, we can substitute this into the equation for the total charge:
q1 + q2 = 8.50 µC
Since q1 and q2 are the same, we can rewrite the equation as:
2q = 8.50 µC
Dividing both sides by 2:
q = 4.25 µC
Therefore, the charge on each point charge is 4.25 µC.
(b) If the force is attractive, then the charges will have opposite signs.
Following the same approach as in part (a), we have:
q1 + q2 = 8.50 µC
But now, the charges have opposite signs, so we can rewrite it as:
q1 - q2 = 8.50 µC
We can substitute this equation and solve for the product of the charges:
0.100 N = (8.99 x 10^9 N·m^2/C^2) * ((q1 * q2) / (0.839 m)^2)
(q1 * q2) = 1.12 x 10^-9 C^2
Now, we substitute the equation into the total charge equation:
q1 - q2 = 8.50 µC
Simplifying, we find:
2q = 8.50 µC
q = 4.25 µC
Therefore, the smallest charge is -4.25 µC and the largest charge is +4.25 µC.