The force of repulsion between two identical negative charges is 3.95 N, when the charges are 35.0 cm apart. What is the magnitude of these charges?
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The force of repulsion between two identical negative charges is 3.95 N, when the charges are 35.0 cm apart. What is the magnitude of these charges?
To find the magnitude of the charges, we can use Coulomb's law, which relates the force between two charged particles to the magnitude of the charges and their separation.
Coulomb's law states that the force of repulsion between two charged objects is directly proportional to the product of their charges 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 between the charges,
k is the Coulomb's constant (8.99 x 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 are given the force of repulsion (F = 3.95 N) and the distance between the charges (r = 35.0 cm = 0.35 m).
Let's substitute the given values into Coulomb's law:
3.95 N = (8.99 x 10^9 Nm^2/C^2) * (q1 * q2) / (0.35 m)^2
Now, we need to solve this equation to find the product of the charges q1 * q2.
Rearranging the equation, we get:
(q1 * q2) = (3.95 N) * (0.35 m)^2 / (8.99 x 10^9 Nm^2/C^2)
Simplifying this expression:
(q1 * q2) = 0.043275397813125 C^2
Now, we need to find the square root of the product of the charges to get the magnitude of each charge.
Taking the square root:
sqrt(q1 * q2) = sqrt(0.043275397813125 C^2)
q1 = sqrt(0.043275397813125 C^2) (since the charges are identical)
Calculating this value:
q1 = 0.208 C
Therefore, the magnitude of each charge is approximately 0.208 C.