Two small charged objects repel each other

Answered question

2022-04-22

Two small charged objects repel each other with a force F when separated by a distance d. If the charge on each object is reduced to 1/4 of its original value and the distance between them is increased 2 times, what will the force between them become?


 

Answer & Explanation

nick1337

nick1337

Expert2023-04-29Added 777 answers

The given problem states that two charged objects repel each other with a force F when separated by a distance d. Let the charge on each object be q and the Coulomb constant be k. Then, the force between the objects is given by Coulomb's law as:
F=kq2d2
Now, it is given that the charge on each object is reduced to 14 of its original value and the distance between them is increased 2 times. Let the new charge on each object be q=14q and the new distance between them be d=2d. Then, the new force between the objects is given by Coulomb's law as:
F=k(14q)2(2d)2
Simplifying the expression, we get:
F=F32
Therefore, the force between the charged objects will become 132 of its original value.

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