Question

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

Answer 1

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

Answer 2

V1 = V2

V = Kq/r

q1/q2 = r1/r2

Let surface charge density be denoted by %.

% = E × 2 × epsilon nought

%1 / %2 = E1 / E2

E = Kq/r^2

%1 / %2 = (r2/r1)^2 × q1/q2

%1 : %2 = r2 : r1.