Two point charges of equal magnitude repel each other with a force of 5.49 Newtons when separated by 15.1 cm. Find the magnitude of the charge (in Coulombs).
same way as the one below that I just did for you
Use meters though 15.1 cm = 0.151 meters
I tried to use your method, it didn't work.
To find the magnitude of the charge, we can use Coulomb's Law, which states that the force of repulsion or attraction between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, Coulomb's Law can be expressed as:
F = k * (q1 * q2) / r^2
where F is the force of repulsion, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the two charges, and r is the distance between them.
In this problem, we know that the force of repulsion (F) is 5.49 Newtons and the distance between the charges (r) is 15.1 cm (which should be converted to meters). We need to find the magnitude of the charge (q).
First, let's convert the distance to meters:
r = 15.1 cm = 0.151 m
Next, we need to rearrange Coulomb's Law to solve for q1 (or q2):
q1 * q2 = (F * r^2) / k
Since both charges have the same magnitude, we can write q1 * q2 as q^2:
q^2 = (F * r^2) / k
Finally, we can solve for q by taking the square root of both sides of the equation:
q = sqrt((F * r^2) / k)
Plugging in the known values:
q = sqrt((5.49 N * (0.151 m)^2) / (9 x 10^9 Nm^2/C^2))
Evaluating this expression will give us the magnitude of the charge in Coulombs.