Question

In: Physics

In the figure particle 1 of charge +q and particle 2 of charge +4q are held...

In the figure particle 1 of charge +q and particle 2 of charge +4q are held at separation L = 8.38 cm on an x axis. If particle 3 of charge q₃ is to be located such that the three particles remain in place when released, what must be the (a) x and (b) y coordinates of particle 3 and (c) the ratio q₃/q?

Expert Solution

Given q1 = q, q2 = 4q and the seperation between them is 8.38cm = 0.0838m. When q3 is placed the three paricles remain in place. That means the net electrostatic foce on q3 by q1 and q2 is zero.

(a) Let q3 be at a distance r from q1. So q3 is at a distance (0.0838-r) from q2. Now the electrostatic foce on q3 by q1 is given by,

The electrostatic foce on q3 by q2 is given by,

Now,

So the co-cordinates of q3 is (2.79, 0).

Therefore, the x-co-ordinate of particle 3 is 2.79cm.

(b) The y-coordinate of particle 3 is 0cm.

(c) Now since they are in equilibrium consider charge q1. Now the electrostatic foce on q1 by q3 is given by,

Similarly the electrostatic foce on q1 by q2 is given by,

Now again,

So the ratio of q3 to q is 0.44.

genius_generous answered 1 year ago

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