# Homework Help: Finding the initial and final charge of two spheres

1. Sep 6, 2011

### fal01

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

Two identical small metal spheres with q1 > 0
and |q1| > |q2| attract each other with a force
of magnitude 70.2 mN, as shown.

The spheres are then brought together until
they are touching. At this point, the spheres
are in electrical contact so that the charges
can move from one sphere to the other until
both spheres have the same ﬁnal charge, q.

After the charges on the spheres have come
to equilibrium, the spheres are moved so that
they are again 1.87 m apart. Now the spheres
repel each other with a force of magnitude
18.954 mN.

Returned to original position
A.)What is the ﬁnal charge on sphere 2? The Coulomb
constant is 8.98755 × 10^9N  m2/C2
002 (part 2 of 2) 10.0 points

B.)What is the initial charge q1 on the ﬁrst
sphere?

2. Relevant equations
F=kq1q2/r^2
x=-b(+/-)sqrt(b^2-4ac)/2a

3. The attempt at a solution

q1 is positive, q2 is negative

F 12 = F 21 = 70.2 mN = -k(q1)(q2)/r²
k = 1/((4)(π)(ε) = 8.9876 x 10^9 m²/c²

70.2mN = -(8.9876 x 10^9)(q1)(q2)/1.87²

after the spheres touch the charge on each sphere is qf = (q1 +q2)/2
F = 18.954 x 10^-3 = (8.9876 x 10^9)(qf²)/1.87²
qf = 2.716 uC
A) 2.716 uC
q1 = -q2 + 2*qf
q1 = -q2 +5.432uC
q1(q2) = 2.73 x10^-11
-q2² + (5.43 x 10^-6)q2 +2.73 x 10^-11 = 0
q2= -+2716 x 10^-6 +/- sqrt(2.95 x 10^-11 + 4(2.73 x 10^-11))/4 = +2.716 +/- 2.944 uC
q2 is negative , so -.288 uC
q1= 5.72 uC
B).?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 6, 2011

### Spinnor

You have answers for q1 and q2. I plugged them in and it looks like they are right. You appear to have answered parts A and B.

???????

3. Sep 6, 2011

### fal01

This is an online homework. It says I got A right but B is wrong. I will go back through and check my math. I just wanted to make sure the process was right.