The figure below shows, in cross section, two solid spheres with uniformly distr

Question

The figure below shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. Point P lies on a line connecting the centers of the spheres, at radial distance 0.52R from the center of sphere 1. If the net electric field at point P is zero, what is the ratio q2/q1 of the total charge q2 in sphere 2 to the total charge q1 in sphere 1? PLEASE SHOW ALL WORK!

The figure below shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. Point P lies on a line connecting the centers of the spheres, at radial distance 0.52R from the center of sphere 1. If the net electric field at point P is zero, what is the ratio q2/q1 of the total charge q2 in sphere 2 to the total charge q1 in sphere 1? nd p

Explanation / Answer

here,

We can treat the charge on sphere 2, and the charge within R/2 in sphere 1, to be at the
centers of the spheres. If q1 and q2 are both positive (or both negative),
they can cancel at P .
We can then equate the magnitudes of the forces:

q2/(3*0.52r)^2 = q1(0.5)^3 / (0.52r)^2

Upon simpification,

0.411 * q2 = q1 * 0.462

q2/q1 = 0.462/0.411

q2/q1 = 1.124

q2 = 1.124 * q1

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