Question

The ratio of charge densities on the surface of two conducting sphere is 2:3

Answer 1

Hey mate here's your answer

“Two conducting spheres of radii r1 and r2 are charged to the same surface charge density. What is the ratio of electric fields near their surface?”

Assuming the media surrounding the spheres have the same permittivity, this ratio will be unity. The radii r1 and r2 do not matter here.

Reason:

Inside the spheres the electric field strengths will be zero, and there will be no tangential components.

The change in the normal component of the dielectric displacement D is equal to the surface charge density, therefor the displacement field terminates perpendicular to the surface charge. Because both spheres have equal surface charge densities, their dielectric displacement fields at the surfaces will be equal, hence their ratio unity. In case of equal permittivities, the electric field ratio will be unity as well.

Update: If the permittivities are not the same, we can deduct from the boundary condition that E2/E1 = ε1/ε2.