"Two small spheres are located 0.50m apart. Both have the same charge on them. If the repulsive force is 5.0N, what charge is on the spheres, in microcoulombs?"
I can begin to use my electrical force formula, but then I have two unknown charges. The anwser is 12 uC, but I am getting numbers like 3.98 x 10 to the -10. Can anyone help please?
5=9E9 q^2/.5^2
q= sqrt 1.39E-10 = 12microC
To solve this problem, you can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's Law is written as:
F = k * (|q1| * |q2|) / r^2
where F is the force between the charges, k is Coulomb's constant (9 * 10^9 N·m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
Given:
Distance (r) = 0.50 m
Force (F) = 5.0 N
Let's solve for the charge magnitude (|q|).
Rearrange Coulomb's Law to solve for |q1| * |q2|:
|q1| * |q2| = (F * r^2) / k
Substitute the given values into the equation:
|q1| * |q2| = (5.0 N * (0.50 m)^2) / (9 * 10^9 N·m^2/C^2)
Calculating the right side:
|q1| * |q2| = (5.0 N * 0.25 m^2) / (9 * 10^9 N·m^2/C^2)
= 1.25 * 10^-9 C
Since the two small spheres have the same charge magnitude, we can now solve for their individual charges.
Let's assume both charges are equal and denote them as |q|.
Therefore, |q1| = |q2| = |q|.
Now we can solve for |q|:
|q|^2 = 1.25 * 10^-9 C
|q| = sqrt(1.25 * 10^-9 C)
|q| ≈ 3.54 * 10^-5 C
Finally, converting the charge to microcoulombs (uC):
|q| = 3.54 * 10^-5 C * (10^6 uC / 1 C)
|q| ≈ 35.4 uC
So, the charge on the spheres is approximately 35.4 microcoulombs (uC).
To find the charge on the spheres, we can start by using Coulomb's Law, which states that the force between two charges is given by the equation:
F = (k * q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant (9 x 10^9 N.m^2/C^2)
q1 and q2 are the charges on the two spheres
r is the distance between the centers of the spheres
In this case, we are given that the force between the spheres is 5.0 N and the distance between them is 0.50 m. Since both spheres have the same charge on them, we can assume that q1 = q2 = q.
Now we can rearrange the equation to solve for the charge on the spheres:
q = (F * r^2) / (k)
Substituting the given values:
q = (5.0 N * (0.50 m)^2) / (9 x 10^9 N.m^2/C^2)
Calculating this will give us the charge in coulombs. To convert it to microcoulombs, we need to multiply by 10^6:
q = ((5.0 N * (0.50 m)^2) / (9 x 10^9)) x (10^6)
Evaluating this expression, we find that the charge on the spheres is approximately 12 microcoulombs (µC).