Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1, Q2​, Q3​, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then what is the ratio of the charges given to the shells, Q1​:Q2​:Q3​, ?

36:9:4

λ = \(\frac{Q}{4\pi R^2}\)

λ ∝ \(\frac{Q}{R^2}\)

$λ_1$ = \(\frac{Q_1}{4πR^{2}}\) ; $λ_2$ = \(\frac{Q_2}{16πR^{2}}\) ; $λ_3$ = \(\frac{Q_3}{36πR^{2}}\)

$λ_1 = λ_2 = λ_3$

Q₁ : Q₂/4 : Q₃/9 = 36Q₁ : 9Q₂ : 4Q₃