Exams › JEE Main › Physics

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?

1. -4
2. -32/25
3. 32/25
4. 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.

Related JEE Main Physics questions

• What is the SI unit of the permittivity of free space, ε₀?
• What is the SI unit used for electric flux?
• A constant electric field E is directed along the positive x-axis. If a charge of 0.5 C is displaced by 2 m along a line inclined at 60° to the x-axis, and the work done in this process is 10 J, what is the magnitude of the electric field?
• An electric dipole is located at the origin O along the x-axis. A point P lies 20 cm from O, and the line OP makes an angle π/3 with the x-axis. If the electric field at P is inclined at an angle θ to the x-axis, what is θ?
• A uniformly charged semicircular wire has radius a and linear charge density λ. The magnitude of the electric field at the centre of the semicircle is
• A point Q is located on the perpendicular bisector of an electric dipole whose dipole moment is p. If Q is at a distance r from the dipole and r is much greater than the dipole size, the electric field at Q varies as

⚔️ Practice JEE Main Physics free + battle 1v1 →