(a) Two point charges totaling 7.50 µC exert a repulsive force of 0.100 N on one another when separated by 0.561 m. What is the charge on each?
F = q1*q2/d^2
so,
q1(7.50*10^-6 - q1)/.561^2 = 0.100
Dropped the k there Steve.
F = kq^2/r^2
q= sqrt(Fr^2/k)
To find the charge on each point charge, we can use Coulomb's law.
Coulomb's law 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.
The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
where:
F is the force between the charges,
k is the electrostatic constant (9.0 x 10^9 N m^2/C^2),
q1 and q2 are the charges on the point charges,
and r is the distance between the charges.
In this problem, we are given:
F = 0.100 N,
r = 0.561 m,
and the total charge is 7.50 µC.
To find the charge on each point charge, we need to divide the total charge by 2, since the force is exerted between two charges of equal magnitude.
Let's substitute the given values into the formula and solve for the charge on each point charge:
To find the charge on each point charge, we can use Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
where:
F is the force between the charges,
k is the electrostatic constant (9.0 x 10^9 N * m^2 / C^2),
q1 and q2 are the charges,
and r is the distance between the charges.
We are given:
F = 0.100 N
r = 0.561 m
k = 9.0 x 10^9 N * m^2 / C^2
Let's plug in these values and solve for the charges:
0.100 N = (9.0 x 10^9 N * m^2 / C^2) * (q1 * q2) / (0.561 m)^2
To solve for the charges, we rearrange the equation:
(q1 * q2) = (0.100 N * (0.561 m)^2) / (9.0 x 10^9 N * m^2 / C^2)
(q1 * q2) = 0.003142 C^2
Since the two charges have the same magnitude, let's assume q1 = q2 = q.
(q)^2 = 0.003142 C^2
Taking the square root of both sides:
q = sqrt(0.003142 C^2)
q ≈ 0.056 C
Therefore, each point charge has a charge of approximately 0.056 C.