Question

Two point charges totaling 9.00 µC exert a repulsive force of 0.200 N on one another when separated by 0.712 m.

What is the charge on each if the force is attractive?

Answer 1

1) Let Q₁ be the charge on first point charge. Then the charge on second point charge is -

Q₂ = (9 - Q₁) C

And according to Coulomb's law, the force between two charges Q₁ and Q₂ separated by a distance of 'r' is -

So, putting value of Q₂ gives -

For, F = 0.2N, r = 0.712m and K = 9 x 10⁹N-m²/C² we have -

This can be written as quadratic equation -

Solving this gives us -

Q₁ = 7.497428528 or Q₁ = 1.502571472

If you put this value to get Q₂, you will see that you get the same set of values.

So, the charge on the point charges are approximately 7.5 C and 1.5 C.

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2)

Now, if the force is attractive then note that one charge will be negative while other will be positive. In that case -

For, F = 0.2N, r = 0.712m and K = 9 x 10⁹N-m²/C² we have -

This can be written as quadratic equation -

Solving this gives us -

Q₁ = 10.113859832592901 or Q₁ = -1.113859832592901.

So, the charge on the point charges are approximately 10.11 C and -1.11 C.

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