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Suppose that there are two solid spheres with uniformly distributed charge throughout their volumes. Each has a radius R. The point P lies on a line connecting the centre of the spheres, with radial distance R/2 from the left sphere (sphere 1). If the net electric field is 0 at P, what is the ratio q2/q1 of the total charge q2 of sphere 2 to total charge q1 of sphere 1? (please explain in detail)

Suppose that there are two solid spheres with uniformly distributed charge throughout their volumes. Each has a radius R. The point P lies on a line connecting the centre of the spheres, with radial distance R/2 from the left sphere (sphere 1). If the net electric field is 0 at P, what is the ratio q2/q1 of the total charge q2 of sphere 2 to total charge q1 of sphere 1? (please explain in detail)

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Grade:12th pass

1 Answers

Sanju
106 Points
3 years ago
Here we can treat the charge on sphere 2, & 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 / (3R/2)2 = q1*(1/2)3 / (r/2)2 
where some constants are cancelled, and charge within R/2 in sphere 1 is q1/8.
Then simplifying the above eqn,
q2/q1 = 9/8.

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