Electric Field/Centripital Force/Gauss law question?

1. Feb 14, 2010

momatik

1. The problem statement, all variables and given/known data

A proton with speed v = 3.42 x 106 m/s orbits just outside a charged sphere of radius r = 0.862 cm. What is the charge in coulombs on the sphere?

2. Relevant equations

(k*q1*q2)/r^2

F = mv^2/r

Gauss Law for sphere, possibly? I'm not sure if I need this.

3. The attempt at a solution

setting the equations equal to eachother and then solving for q2

kq1q2/r2 = mv^2/r

rearranged...

q2= mv^2r/kq1

m = mass of proton = 1.672e-27
q1 = charge of proton = 1.602e-19
v = 3.42e6
r = .00862 m

Values subbed in...

q2 = [(1.672e-27)*(3.42e6^2)*(.00862)] / [(9e9)*(1.602e-19)]

I get 1.1696e-7 which is incorrect.

Last edited: Feb 14, 2010
2. Feb 15, 2010

gabbagabbahey

I haven't checked your numbers, but you seem to be forgetting that force is a vector, not a scalar. You need to consider the direction of both the centripetal and Coulomb forces....what sign must q2 be for the Coulomb force to be responsible for the centripetal acceleration of the proton?

3. Feb 16, 2010

momatik

Wow Yeah, the answer simply had to be negative. I justifiably feel pretty stupid right now.