Solving Simple Transposition Problem for Charge Separation in Air

[MattNotrick]

Homework Statement

I am trying to tranpose a given value but it seems I am getting the wrong answer what ever route I am taking, please can someone correct me.

The question is Two point charges A and B have values of 5x10^-6C and 7x10^-6C. Calculate the separation (R) when the force between them is 3.2N of air.

I am given all these values so I end up with the equation below.

Homework Equations

F=Force
Q1=Charge
Q2=Charge
Eo=Air
Er=Permitivty of Free Space
R^2= separation
π= pi

The Attempt at a Solution

F=Q1Q2/4πEoErR^2

I am trying to transpose for R^2

F4πEoErR^2 = Q1Q2/F4πEoEr

R^2 = Q1Q2/F4πEoEr

R = √[Q1Q2/F4πEoEr]

(Inputting the Values_

R = √[(5x10^-6)(7x10^-6) / 3.2 * 4π * 8.85x10^-12 * 1]

R = 3.4876x10^-11

I think I messed up my transposition somewhere because the rest of the answers I've been doing have been like 0.5m - 3m separation, but I maybe be wrong. I've been doing 8 hours a day revision all week so my heads all over the place.

Thank you.

 

[Apphysicist]

Looks like some kind of calculator error: if you notice, 10^-6*10^-6/10^-12 will cancel so you're clearly off by orders of magnitude.

 

[MattNotrick]

Hey, thanks for the fast reply but I am not sure I understand what you are saying. Can you verify if all the steps of the transposition are correct, or if they are what error I have made?

Thanks again

 

[Apphysicist]

Hey, thanks for the fast reply but I am not sure I understand what you are saying. Can you verify if all the steps of the transposition are correct, or if they are what error I have made?

Thanks again

Solving for R looks fine:

F=kqq/r^2
r^2*F=kqq
r=sqrt(kqq/F) ; k=1/(4*pi*E_o*E_r)

I'm saying you may have put the values in your calculator incorrectly.

 

[Zryn]

I would hazard a guess that you went wrong here:

R = √[(5x10^-6)(7x10^-6) / 3.2 * 4π * 8.85x10^-12 * 1]

Try sticking another pair of brackets in:

R = √[ {(5x10^-6)(7x10^-6)} / {3.2 * 4π * 8.85x10^-12 * 1} ]

Your equation is correct, and given the numbers I get a vastly different solution to you. When I don't use the extra pair of brackets, I get your answer!