two charges of equal magnitude are 25.5 cm apart if the force between the charges is 155 N what is the magnitude of the charges
3.20*10^-5
The force between two identical charges separated by 1 cm is equal to 90 N. What is the
magnitude of two charges?
To find the magnitude of the charges, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's law formula:
F = k * (q1 * q2) / r^2
where:
F = force between the charges
k = Coulomb's constant (9 * 10^9 N m^2/C^2)
q1 and q2 = magnitudes of the charges
r = distance between the charges
Given:
F = 155 N
r = 25.5 cm = 0.255 m
We can rearrange the formula to solve for the magnitude of the charges:
q1 * q2 = (F * r^2) / k
Substituting the given values:
q1 * q2 = (155 * (0.255)^2) / (9 * 10^9)
Calculating:
q1 * q2 ≈ 3.246 * 10^-9 C^2
Since the charges have equal magnitude, we can write:
q1^2 = 3.246 * 10^-9
Taking the square root of both sides:
q1 ≈ √(3.246 * 10^-9)
Calculating:
q1 ≈ 5.69 * 10^-5 C
Therefore, the magnitude of the charges is approximately 5.69 * 10^-5 C.
To find the magnitude of the charges, we can use Coulomb's law, which states that the force between two charges is given by:
F = (k * |q1 * q2|) / r^2
where F is the force between the charges, k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, we have the following information:
F = 155 N (force between the charges)
r = 25.5 cm = 0.255 m (distance between the charges)
k = 9 × 10^9 Nm^2/C^2 (electrostatic constant)
To find the magnitudes of the charges (q1 and q2), we rearrange Coulomb's law equation:
|q1 * q2| = (F * r^2) / k
Now we can substitute the given values:
|q1 * q2| = (155 N * (0.255 m)^2) / (9 × 10^9 Nm^2/C^2)
Simplifying the equation gives:
|q1 * q2| = 1.4695 × 10^-4 C^2
Since the charges have equal magnitudes, we can assume q1 = q2 = q, which means:
q^2 = 1.4695 × 10^-4 C^2
Taking the square root of both sides:
q = √(1.4695 × 10^-4 C^2)
q ≈ 0.01208 C
Therefore, the magnitude of the charges is approximately 0.01208 Coulombs.