two small spheres lie 1.5 meters apart and carry identical charges. How large is the charge on each if a sphere experiences a force of 2.0 N.
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To determine the charge on each sphere, you can use Coulomb's Law, which describes the relationship between the force between two charged objects, the charges on the objects, and the distance between them. Coulomb's Law is given by:
F = k * (|q1 * q2| / r^2)
where:
- F is the force between the two charged objects,
- k is the electrostatic constant (k ≈ 9.0 x 10^9 Nm^2/C^2),
- q1 and q2 are the charges on the two objects, and
- r is the distance between the centers of the two objects.
In this case, the force F is given as 2.0 N, and the distance r is given as 1.5 meters. Since the charges on the two spheres are identical (meaning both charges are the same value, but with different polarities), we can denote the charges as q for both spheres.
Rearranging Coulomb's Law to solve for the charge q, we have:
q = √((F * r^2) / k)
Substituting the given values, we get:
q = √((2.0 * 1.5^2) / (9.0 x 10^9))
Calculating this equation, we find:
q ≈ 3.1 x 10^(-6) C
Therefore, each sphere carries a charge of approximately 3.1 microcoulombs.