Two charged particles, with charges and , are located at a distance apart on the

Question

Two charged particles, with charges and , are located at a distance apart on the x axis. A third charged particle, with charge , is placed on the x axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3. Find the position of charge 3 when = 2.00 .The key equation for this problem is . In the previous part, you solved it by applying Coulomb's law and obtaining a quadratic equation with two real-valued solutions for . If, instead of writing an equation for , you apply Coulomb's law and write a simpler equation in terms of the distances of charge 3 from charges 1 and 2, respectively, and , which of the following relations would you get?

Explanation / Answer

Magnitudes are given by

q1q3/(r13)2 and

q2q3/(r23)2,

q1q3 is 1/4 the same as q2q3 .

Therefore, r23 must be twice what r13 is, to make these magnitudes the same. i.e

q*q/(r13)2 = q*4q/(r23)2, so that 1/(4r132) = 4/(4r232)

==> r232 = 4r132
==> r23 = 2*r13

We have two possibilities: q3 is between q1 and q2, or (reading left-to-right) their positions are q3, q1, q2.

q3 Between:
We know that r12 = 2.00 cm.

Also, r13 + r23 = r12,

so that r13 + 2*r13 = 2 cm,

and so r13 = 0.66 cm.

Here, q3 is 1/3 of the way between q1 and q2.

q3 to the left:
We know that r12 = 2.00 cm.

Also, r13 + r12 = r23,

so that r13 + 2 cm = 2 r13.

Thus, r13 = 2cm.

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