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oddlogic
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Homework Statement
There is a charge located at the origin of magnitude 5nC. There exists a vertical line of charge, 2 meters in length, that runs from (2m,-1m) to (2m,1m).
a) What uniform linear charge density must this line of charge have in order that the net force on a charge placed at (5.0m, 0m) has no net force acting on it?
b) What would be the voltage at this point?
c) aside from x = +/- (infty), where (if at all) would the voltage be zero?
Q1= 5nC. I called the line charge Q2. This could be very wrong. Q3 is the unknown.
Homework Equations
F = (Q1Q2)/r^2
(delta)V = Ke(integral) dq/r
dq = (lambda)(dx)
The Attempt at a Solution
I treated the line charge as a point charge by saying:
F13 - F23 = 0 (the force of 1 on three and the force of the line charge acting on 3 must be zero)
This meant that the total charge for Q2 was -1.8nC. To find rho (charge density) I just took 1.8nC and divided by 2, since that is the length of the line of charge.
part b is a little trickier but I think it must be something akin to integrating from -1 to 1 for the integral of (Ke)(dq)/(y), but that doesn't seem quite right since we have Q3 to think about and also because "r" (which in this equation is "y") changes as we go from -1 to 1, so r must be something besides just "y". Obviously, dq is now (lambda)(dy). Ke and lambda are constants, so it should just be dy/r, whatever r is. could r = [(1-y)^2 + 4]?
I have seen (and know how to solve) point charge problems on an X axis that look a lot like this, but the fact that the Q3 is unknown (and my method for solving for Q2 could be wrong) and the y integration is kind of throwing me. Help? (but not too much)
Thanks,
Brad