How Do You Calculate Charges in Electrostatic Force Problems?

[roseyramos]

Homework Statement

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.0898 N when their center-to-center separation is 39.6 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0337 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive charge in coulombs on the other?




A particle of charge Q is fixed at the origin of an xy coordinate system. At t = 0 a particle (m = 0.931 g, q = 4.49 µC is located on the x-axis at x = 16.0 cm, moving with a speed of 36.1 m/s in the positive y direction. For what value of Q (in μC) will the moving particle execute circular motion? (Neglect the gravitational force on the particle.)

Homework Equations

The Attempt at a Solution

So centripal force is

Fc=m•a=m•v²/R

And the electrostatic force is

Fe = kQq/R²

They are equal.


I need to get the answer is nanoCouloumbs. When I set these equations equal I get Q=481, but I have to remember that it's negative. The answer is supposed to be in NanoCoulombs, so I don't know if I'm correct and am typing it in wrong or I am way off. It's for one of the online physics homework thing we use at USD, so there's no way for me to know if I'm way off or almost there.

For part A, some other students think it's impossible, but the website is asking for an exact number for each one. I thought I did that one right as well, but what I'm getting is not correct. Can anyone help?

 

[rl.bhat]

Hi roseyramos,
Welcome to PF.
Let Q1 and -Q2 be the charges on the spheres. Using the relevant formula find -Q1*Q2.
When you join them by a wire and separate to the original position, the charge on each sphere will be (Q1 - Q2)/2.
Again using the relevant find [(Q1 - Q2)/2.]^2.
Using these values find Q1 and Q2