Two charged spherical conductors of radii r1 and r2


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two charged spherical conductor of radius R1 and R2 when connected by a conducting wire acquire charges Q1 and Q2 find the ratio of their charge density in terms of radius

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The potenital will become , as they are connected with wire.So, V1=V2
q1/4πε₀R1=q2/4πε₀R2
q1/q2=R1/R2-----(1)
surafce charge densities are
 
σ₁/σ₂ =(q1/4πR1²)/(q2/4πR2²)
⇒(q1/q2 )x(R2²/R1²)
⇒(R1/R2)x(R2²/R1²)
⇒R2/R1
σ₁/σ₂=R2/R1

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