Consider two point charges a distance 1.5 cm apart. These charges have an electric potential energy of -190 micro J. The total charge of the system (the sum of the two charges) is 26 nC. What is the charge of each point charge?
Uelec = K*q1*q2/d (d = distance b/w the two charges, q1 and q2)
q1+q2 = qtot = 26*10^-9C
The Attempt at a Solution
From the above equation, q1=qtot-q2.
Plugging this into the electric potential energy equation gives Uelec = K*(qtot-q2)*q2/d.
Simplifying gives the quadratic equation 0 = -q2^2+qtot*q2-U*d/K.
q2 = (-qtot +- sqrt(qtot^2-4*U*d/K)/)-2
When I solve this, I get the two answers 35*10^-9C and -9*10^-9C, which plug back into the Uelec equation correctly. However, they are incorrect.
I talked to my TA, who has the general masteringphysics answers, and he told me this:
q1 = (q + sqrt(q^2 - 4*U*d/K))/2 *10^-9 and q2 = (q - sqrt(q^2 - 4*U*d/K))/2 *10^-9. When I ignore the 10^-9 on the end and plug in 26*10^-9 for q, I get the same answers as I got on my own. When I plug in 26 for q and add the *10^-9 on the end, I get 26nC for one charge and zero for the other. That doesn't really make sense to me so I'm not sure what's going on there, or maybe I'm plugging the wrong values into the general solution equation. I have been very careful with plugging in the correct micro/nano/etc. numbers, and meters instead of cm, and still have the wrong answers. I'd really appreciate some help. Thanks!
Edit: Actually I just got this correct, I entered my answers backwards before and put q1 where masteringphysics wanted q2.