Coulomb help please? Balloon is rubbed with wool giving it a charge of -8.9x10^-14 C. What is the force between balloon and a metal sphere that is charged 25 C and is 2 km away?

Question

anonymous · Answer

I tried setting up the equation but I think its terribly wrong. F=8.9* -8.9x10^-14/2,000 m ?

anonymous · Answer

Mostly there :) You set up the electric potential of the balloon at 2km
$$V_{balloon} = k\frac{q_{balloon}}{r} $$

To get the force between two charged objects you have
$$ F_{coulomb} = k\frac{q_1q_2}{r^2} $$

anonymous · Answer

Ahhh! I always get confused! >.< I thought that r2 was always supposed to be converted into meters?

anonymous · Answer

You're right :)  You do need to convert the "r" into meters because of the constant, K you put in front.  

K is in units of Newton*meters^2/Coulomb^2
$$ K \propto \frac{N \ m^2}{C^2}$$

So to get units of Force - Newtons -  you have to multiply it by Coulomb^2/m^2, so that's what you do! 
$$ \frac{q_1q_2}{r^2} \propto \frac{C*C}{m^2}$$

If you leave r in km, your answer here will be off by a magnitude of 1x10^-6 :P

anonymous · Answer

Will my answer be 5.0x10^-9 N ? @AllTehMaffs

anonymous · Answer

Indeed!

anonymous · Answer

Thanks for the help! Much appreciated (: