How do I determine the distance between the charges if the force is doubled?

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Offline Chikis

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Two equal point charges exert a force F1 on each other when they are [tex]5.0\times10^{-2}m[/tex] apart in a vacuum. Determine the distance between the charges if the force is to be doubled.

The electric force between two point charges is given as [tex]F\alpha \frac{q1q2}{r^2}[/tex]
where q1 and q2 are the charges, F= force and r = distance apart.

Since the force is inversly proportional to the square of the distance apart, if the force is doubled, then the square of the distance apart will be reduced by 2.

[tex]\rightarrow;r^2=\frac{5.0\times10^{-2}\times5.0\times10^{-2}}{2}= \frac{25\times10^{-4}}{2\times10^0}=1.25\times10^{-3}m[/tex]

But am not too sure of my  answer. Please I need help in tackling this problem.
« Last Edit: 09/07/2014 08:52:48 by Chikis »

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Offline evan_au

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the square of the distance apart will be reduced by 2
You are right that the square of the distance must be halved.

Another way of saying this is that the distance must be reduced by the square root of 2, which is approximately 1.414.

50mm divided by 1.414 is roughly 35mm.

This is the answer in words. If this is a homework assignment, you will need to work out the answer as an equation, and provide it to more decimal places...

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Offline Chikis

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the square of the distance apart will be reduced by 2
Another way of saying this is that the distance must be reduced by the square root of 2, which is approximately 1.414.

50mm divided by 1.414 is roughly 35mm.

This is the answer in words. If this is a homework assignment, you will need to work out the answer as an equation, and provide it to more decimal places...

 
You are right that the square of the distance must be halved.

I don't think am right. If am right, why am I having the result as [tex]1.25\times10^{-3}m[/tex] and you are having yours as 3.5m?

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Offline evan_au

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The square of the distance is 1.25x10-3 meters2.

But we don't measure distances in meters2, we use meters.

Take the square root of 1.25x10-3 meters2 to give a distance of 3.5x10-2 meters = 35 millimeters.

So the two answers agree, when you use the appropriate units.

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Offline Chikis

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Thank you. Am cleared now.