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

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#### Chikis

• Jr. Member
• 35
##### How do I determine the distance between the charges if the force is doubled?
« on: 07/07/2014 09:42:02 »
Two equal point charges exert a force F1 on each other when they are $$5.0\times10^{-2}m$$ 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 $$F\alpha \frac{q1q2}{r^2}$$
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.

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

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 »

#### evan_au

• Neilep Level Member
• 4319
##### Re: Determine the distance between the charges if the force is to be doubled.
« Reply #1 on: 08/07/2014 08:35:11 »
Quote
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...

#### Chikis

• Jr. Member
• 35
##### Re: Determine the distance between the charges if the force is to be doubled.
« Reply #2 on: 08/07/2014 21:57:53 »
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 $$1.25\times10^{-3}m$$ and you are having yours as 3.5m?

#### evan_au

• Neilep Level Member
• 4319
##### Re: How do I determine the distance between the charges if the force is doubled?
« Reply #3 on: 09/07/2014 10:22:34 »
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.

#### Chikis

• Jr. Member
• 35
##### Re: How do I determine the distance between the charges if the force is doubled?
« Reply #4 on: 10/07/2014 01:36:21 »
Thank you. Am cleared now.