- #1
Saladsamurai
- 3,020
- 7
!Coulomb's Law!
So I have already solved this one before, but I was redoing it fir practice when I encountered something that is troubling me. Depending on how I choose to solve my two equations, I get different results. Surely I am doing something wrong, but I cannot see it.
Problem
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of .108 N when their center-to-center separation is 50 cm. The spheres are then connected by a thin conducting wire. When the wire is disconnected, the spheres repel each other with an electrostatic force of .036 N. Of the initial charges on the spheres, with a positive net charge, what was the (a) negative charge of one of them and (b) the positive charge of the other?
Now I have used conservation of charge for after they connect and I end up with two equations and two unknowns:
[tex]F_e=\frac{kq_1q_2}{r^2}\Rightarrow q_1q_2=3.00(10^{-12})[/tex] (1)
[tex]F_e'=k\frac{(\frac{q_1+q_2}{2})^2}{r^2}\Rightarrow q_1+q_2=2.00(10^{-6})[/tex] (2)
Attempt 1:
If I solve (2) for q_1 then [itex]q_1=2(10^{-6})-q_2[/itex]
plugging the above into (1) [itex] -q_2^2+2(10^{-6})q_2-3(10^{-12})=0[/itex] gets me a nonreal answer.
Attempt 2:
BUT if I solve (1) for q_1 then [itex]q_1=\frac{3(10^{-12})}{q_2}[/itex] and plugging that into (2) I get [itex]q_2^2-2(10^{-6})q_2-3(10^{-12})=0[/itex] which solves correctly.
I am consistently of by a sign in the first attempt. Can anyone see what the problem is?
So I have already solved this one before, but I was redoing it fir practice when I encountered something that is troubling me. Depending on how I choose to solve my two equations, I get different results. Surely I am doing something wrong, but I cannot see it.
Problem
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of .108 N when their center-to-center separation is 50 cm. The spheres are then connected by a thin conducting wire. When the wire is disconnected, the spheres repel each other with an electrostatic force of .036 N. Of the initial charges on the spheres, with a positive net charge, what was the (a) negative charge of one of them and (b) the positive charge of the other?
Now I have used conservation of charge for after they connect and I end up with two equations and two unknowns:
[tex]F_e=\frac{kq_1q_2}{r^2}\Rightarrow q_1q_2=3.00(10^{-12})[/tex] (1)
[tex]F_e'=k\frac{(\frac{q_1+q_2}{2})^2}{r^2}\Rightarrow q_1+q_2=2.00(10^{-6})[/tex] (2)
Attempt 1:
If I solve (2) for q_1 then [itex]q_1=2(10^{-6})-q_2[/itex]
plugging the above into (1) [itex] -q_2^2+2(10^{-6})q_2-3(10^{-12})=0[/itex] gets me a nonreal answer.
Attempt 2:
BUT if I solve (1) for q_1 then [itex]q_1=\frac{3(10^{-12})}{q_2}[/itex] and plugging that into (2) I get [itex]q_2^2-2(10^{-6})q_2-3(10^{-12})=0[/itex] which solves correctly.
I am consistently of by a sign in the first attempt. Can anyone see what the problem is?