Calculating Force Between Three Insulated Conductors with Equal Charges

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SUMMARY

The discussion centers on calculating the force between three insulated conductors, A, B, and C, each carrying equal positive charges of 5.77x10^-9C. The force exerted by A on B is 2.5 microNewtons, while the force between B and C, calculated incorrectly as 750 microNewtons, is actually 7.5 microNewtons. The error arose from incorrect unit conversion and the order of operations in the calculations. The correct approach involves ensuring proper conversion from centimeters to meters before applying Coulomb's law.

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Ok, the question is:

A, B and C are three small insulated conductors all carrying positive charges of equal size. A exerts a force of 2.5microNewtons on B. The distance between A and B is 2\sqrt{3}cm and the distance between B and C is 2cm. What is the magnitude of the force exerted by B on C?

I know how to do all of it, since all the charges are the same, I've worked out the charge of A, B and C to be 5.77x10^-9C (I've checked and re-checked again)

So then I worked out the force between B and C and I continually get 7.5x10^-4N. When converting this to microNewtons, it is 750microNewtons.

According to the textbook however, I am wrong and by two decimal points actually. Apparently, the answer is 7.5microNewtons.

I've checked time and time again, made sure that I converted the microNewtons to Newtons (SI units) when calculating and converting the cm to m in regard to SI units. I don't know what I've done wrong. Could someone please check for me, because the textbook is prone to errors sometimes.
 
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I got 7.5 micro Newtons.
So please show your calculations.
I can rewrite the above question in this way.
Two identical charges repel each other with a force of 2.5 micro Newton when they separate by a distance 2*sqrt3 cm. If their distance is 2 cm, what is the new force of repulsion?
 
Don't worry, I know what I did wrong. I squared 2*sqrt3 and THEN divided by 100 which I wasn't meant to do. I had to do it the other way round.

Such small mistakes are quite costly.
 

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