- #1
RM86Z
- 23
- 6
- Homework Statement
- Particles of charge Q and 3Q are placed on the x axis at x = -L and x = +L, respectively. A third particle of charge q is placed on the x axis, and it is found that the total electric force on this particle is zero. Where is the particle?
- Relevant Equations
- F = kq1q2/r^2; q1 and q2 are two charges, k is Coulomb's constant and r is the separation between the two charges.
I am stumped by this one! My attempt at solving this problem was to do a coordinate transform to put Q at the origin and 3Q at 2L on the x-axis. The distance then between q and Q is x and the distance between q and 3Q is (2L - x).
The electrical force between q and Q is F1 = kqQ/x^2.
The electrical force between q and 3Q is F2 = kq3Q/(2L - x)^2.
The net force on q is zero which implies that F1 = -F2.
F1 = -F2
kqQ/x^2 = -kq3Q/(2L-x)^2
(2L - x)^2 = -3x^2
4L^2 - 4Lx +4x^2 = 0
L^2 - Lx + x^2 = 0
This has no real solutions.
What am I doing wrong here?!
Thank you!
The electrical force between q and Q is F1 = kqQ/x^2.
The electrical force between q and 3Q is F2 = kq3Q/(2L - x)^2.
The net force on q is zero which implies that F1 = -F2.
F1 = -F2
kqQ/x^2 = -kq3Q/(2L-x)^2
(2L - x)^2 = -3x^2
4L^2 - 4Lx +4x^2 = 0
L^2 - Lx + x^2 = 0
This has no real solutions.
What am I doing wrong here?!
Thank you!