If the charges on the two spheres are equal, each sphere has a charge of approximately 0.06 Coulombs.
- If the charge on the first sphere is one-quarter the charge of the second sphere, the charge on the second sphere is approximately 0.12 Coulombs.
To find the charge on each sphere, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two charged objects is given by the equation:
F = k * (|q1| * |q2|) / r^2
where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 N*m^2/C^2), |q1| and |q2| are the magnitudes of the charges on the two spheres, and r is the distance between them.
In the given problem, the force (F) between the two spheres is 0.215 N and the distance (r) between them is 15.2 cm (or 0.152 m).
First, let's assume that the charges on the two spheres are equal. We can substitute the known values into the Coulomb's Law equation:
0.215 N = (8.99 x 10^9 N*m^2/C^2) * (|q1| * |q1|) / (0.152 m)^2
Simplifying this equation, we find:
|q1|^2 = (0.215 N * (0.152 m)^2) / (8.99 x 10^9 N*m^2/C^2)
|q1|^2 ≈ 0.00363 C^2
Taking the square root of both sides, we get:
|q1| ≈ 0.06 C
Therefore, if the charges on the two spheres are equal, each sphere has a charge of approximately 0.06 Coulombs.
Now, let's consider the scenario where the charge on the first sphere is one-quarter the charge of the second sphere. Let's assume the charge on the second sphere is q2.
Using the same equation and substituting the known values:
0.215 N = (8.99 x 10^9 N*m^2/C^2) * ((1/4) * q2 * q2) / (0.152 m)^2
Simplifying this equation, we find:
q2^2 = (4 * 0.215 N * (0.152 m)^2) / (8.99 x 10^9 N*m^2/C^2)
q2^2 ≈ 0.0145 C^2
Taking the square root of both sides, we get:
q2 ≈ 0.12 C
Therefore, if the charge on the first sphere is one-quarter the charge of the second sphere, the charge on the second sphere is approximately 0.12 Coulombs.