In the figure particle 1 of charge q 1 = 1.01 ?C and particle 2 of charge q 2 =
ID: 1259695 • Letter: I
Question
In the figure particle 1 of charge q1 = 1.01 ?C and particle 2 of charge q2 = -2.93 ?C, are held at separation L = 10.1 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a)x and (b)y coordinates of particle 3?
In the figure particle 1 of charge q1 = 1.01 ?C and particle 2 of charge q2 = -2.93 ?C, are held at separation L = 10.1 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a)x and (b)y coordinates of particle 3?Explanation / Answer
Since q1 and q2 are opposite charges the is no point in between them where the net force is zero. Since the magnitude of q2 is > q1 then q3 must be located to the left of q1.
The net force will be zero where the total electric field is zero.
Let r be the distance from q1 so E1 = k*q1/r^2
Now E2 = k*q2/(r + .11)^2
So k*q1/r^2 = k*q2/(r + .101)^2 ...so q1*(r + .101)^2 = q2*r^2
So (q2 - q1)*r^2 -2*q1*.11*r -q1*.101^2 = (2.93x10^-6 -1.01x10^-6)*r^2 - .202*1.01x10^-6*r - 0.01020*q1 = 0.... 1.93x10^-6*r^2 - 2.04x10^-7*r - 1.0302x10^-8 = 0
0.143m So x = -0.143m and y = 0
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