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Physics help?
A positive charge q1 = 1.03 μC is fixed at the origin, and a second charge q2 = -2.63 μC is fixed at x = 10.3 cm.
Where along the x-axis should a third charge be positioned so that it experiences no force?
1 Answer
- nyphdinmdLv 75 years ago
q1 is at x1 = 0) and q2 is at x2 = 0.103 m The third charge q has to see a net electric field of zero in order to have no force exerted on it. So Let's add the electric fields from q1 and q2 at some point x
E_net = 0 = kq1/x^2 + kq2/(x - x1)^2 divide out k, put over common denominator, and multiply away denominator
0 = q1(x-x1)^2 + q2x^2 = (q1 +q2)x^2 - 2q1x1 x + q1 x1^2 = x^2 - (2q1*x1/Q) x + q1 x1^2/Q
where Q = q1 + q2
Now use quadratic formula to find x
x = q1/Q +/- sqrt((q1x1/Q)^2 - q1x1^2/Q)
Plug in the values for q1, q2 and x1 and remember there are two values of x - one for the "+" in the formula above and the other for the "-"
