Two stationary point charges of +61.0µC and +0.48µC exert a repulsive force on each other of 172N. What is the distance between the two charges?
the electrostatic force equation will solve all your problems
To find the distance between two point charges, you can use Coulomb's Law, which relates the force between two charges to their magnitudes and the distance between them. Coulomb's Law is given by:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant, approximately equal to 9 x 10^9 Nm^2/C^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges.
In this case, we are given the force between the charges as 172N, and the magnitudes of the charges as +61.0µC and +0.48µC. We need to find the distance (r) between the two charges.
Plugging in the given values into Coulomb's Law, we get:
172 = (9 x 10^9) * ((61.0 x 10^-6) * (0.48 x 10^-6)) / r^2
Now we just need to solve for r.
First, we can simplify the expression on the right side of the equation:
172 = (9 x 10^9) * (29.28 x 10^-12) / r^2
Next, let's multiply both sides of the equation by r^2 to isolate it:
172 * r^2 = (9 x 10^9) * (29.28 x 10^-12)
Dividing both sides of the equation by (9 x 10^9) * (29.28 x 10^-12), we get:
r^2 = (172) / ((9 x 10^9) * (29.28 x 10^-12))
Calculating the right side of the equation, we get:
r^2 = 0.001942
Now, to solve for r, we take the square root of both sides:
r = √0.001942
Calculating the square root, we find:
r ≈ 0.044 m
Therefore, the distance between the two charges is approximately 0.044 meters.