Calculating Force Between Three Insulated Conductors with Equal Charges

[Procrastinate]

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.

 

[rl.bhat]

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?

 

[Procrastinate]

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.