Question

A spherical shell of radius Ra and a solid metal sphere of radius Rb(Ra>Rb)are kept apart and each is given a charge +Q

If the two are connected by a metal wire what is the relation between electric field on their surfaces and ratio between surface charge density

Answer 1

Electric field inside a spherical metallic shell with charge on the surfaceis always zero.

When the sells are connected with a thin metal wire then electric potentials will be equal, say V
∴ 1/ 4πϵ₀ Q_A/R_A = 1 / 4 πϵ₀ Q_B­/R_B = V
As R_A> R_B therefore Q_A> Q_B­
As σA/σB
=>QA/4πR²A /QB/4πR²_B
= R²_B / R²_A * 4πϵ₀ R_AV / 4πϵ₀ R_AV
∴σ_A/σ_B = R_B / R_A

Also E_A = σ_A/ σ_B = R_B/R_A< 1 ∴ E_A< E_B