Two charged particles repel each other with a force F. If the charge of one of the particles is doubled and the distance between them is also doubled, then the force will beGroup of answer choicesF/2.F/4.2F.F.
Question
Two charged particles repel each other with a force F. If the charge of one of the particles is doubled and the distance between them is also doubled, then the force will beGroup of answer choicesF/2.F/4.2F.F.
Solution
The force between two charged particles is given by Coulomb's law, which states:
F = k * |q1*q2| / r^2
where:
- F is the magnitude of the force between the charges,
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges, and
- k is Coulomb's constant.
According to the problem, the charge of one of the particles is doubled and the distance between them is also doubled. Let's denote the initial charge of the first particle as q1, the initial charge of the second particle as q2, and the initial distance as r. After the changes, the new charge of the first particle is 2q1, the charge of the second particle remains q2, and the new distance is 2r.
Substituting these values into Coulomb's law gives the new force F':
F' = k * |2q1q2| / (2r)^2 = k * 2|q1q2| / 4r^2 = F/2
So, the new force is F/2.
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