The surface densities on the surfaces of two charged spherical conductors of radii R1 and R2 are equal. The ratio of electric intensities on their surfaces is

Question. The surface densities on the surfaces of two charged spherical conductors of radii R₁ and R₂ are equal. The ratio of electric intensities on their surfaces is:

a) R₁² / R₂²

b) R₂² / R₁²

c) R₁ / R₂

d) 1 : 1

Answer: d) 1 : 1

Let the surface densities on the surfaces of two charged spherical conductors of radii R1​ and R2​ be σ1​ and σ2​ respectively.

But σ1​=σ2​  …(given)Electric field intensity on surface of spherical conductor is given by,

E=Q/4πϵ_o​r²​=​σ/ϵ_o

∴ Ratio of electric field intensities on their surfacesis given by,

E1/E2 =​​ σ₁/ϵ_o/​​ σ₂/ϵ_o​ =σ1​​ /​​ σ₂ = 1/1 …(σ1​=σ2​)

∴E1​:E2​=1:1