- #1
msbell1
- 25
- 0
Homework Statement
Two charges, q1 and q2, are separated by a distance r. Find the position at which a third charge, q3, can be placed so that the net electrostatic force on it is zero.
Homework Equations
Coulomb's Law:
F = (kq1q2)/r122 * (r12hat)
The Attempt at a Solution
I was trying to solve this for the general case, without making any assumptions about the relative signs of q1 and q2. However, this kind of turns into a mess (for me at least), so I changed my strategy. I now consider two cases. One is where q1q2>0 (they have the same sign. In this case, I know that q3 will have to be placed somewhere between q1 and q2. This gives me (after assigning q1 to the origin, and q2 to x=r, and placing q3 at position x),
(kq1q3)/x^2 = (kq2q3)/(r-x)^2
Solving this for x, I find:
x = [(q1 (+or-) sqrt(q1q2))/(q1-q2)]*r
This looks kind of ok, except, what happens when q1=q2? That doesn't make any sense. It would look better if it was (q1+q2) in the denominator. Then I thought maybe I messed up a sign in my original equation, so I tried
(kq1q3)/x^2 = -(kq2q3)/(r-x)^2
(I just put a minus sign in front of the term on the RHS.) This equation actually seems like it should be appropriate when q1q2<0 (the have opposite signs). Solving this gives:
x = [(q1 (+or-) sqrt(-q1q2))/(q1+q2)]r,
and this equation has perfect behavior for the case where it is valid, when q1q2<0.
Can anyone see what I did wrong in the first solution? I know if q1=q2 I should get x=r/2, not x=∞. Thanks!