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Two non-conducting solid spheres of radii R and 2R carry uniform volume charge densities rho1 and rho2 respectively and touch each other externally. Along the line joining their centres, the net electric field at a point a distance 2R from the centre of the smaller sphere is zero. What value(s) can the ratio rho1/rho2 take?
- -4
- -32/25
- 32/25
- 4
Correct answer: -4
Solution
This is a classic JEE 2009 problem with two valid geometries depending on which side of the small sphere the test point lies. Setting the fields of the two spheres equal and opposite for the point at distance 2R from the small centre gives rho1/rho2 = -4 (and the alternate placement gives -32/25). The negative sign means the densities must be opposite for cancellation.
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