n the figure below, particles 1 and 2 of charge q1 = q2 = +4.80 10-19 C are on a

Question

n the figure below, particles 1 and 2 of charge q1 = q2 = +4.80 10-19 C are on a y axis at distance d = 34.0 cm from the origin. Particle 3 of charge q3 = +9.60 10-19 C is moved gradually along the x axis from x = 0 to x = +5.0 m. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes?



(b) position of maximum force


_________________m




(d) magnitude of maximum force


_______________________N

Explanation / Answer

by symmetry only x component will matter.
so
F =2 k q1 q2 /r^2 cos

r= sqrt( d^2 + x^2)

and cos = x/r

so

F = 2 k q1 q2 x/ (d^2 + x^2)^3/2

F= 2 * 9E9 * 4.8E-19 *9.6E-19 * x/(34E-2^2 + x^2)^(3/2)

plot this from 0 to 5 to find maximum

max at x = 5

F = 1.02E-30 N

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