An insulating solid sphere of the radius R is charged in a non-uniform manner such that the volume charge density ρ = A r , where A is a positive constant and r is the distance from the centre. The potential difference between the centre and surface of the sphere is

Question

An insulating solid sphere of the radius R is charged in a non-uniform manner such that the volume charge density ρ = A r , where A is a positive constant and r is the distance from the centre. The potential difference between the centre and surface of the sphere is, A R 8 ε 0, A R 4 ε 0, A R ε 0, A R 2 ε 0

MARKS App · Accepted Answer

E × 4 π r 2 = q ε 0 E × 4 π r 2 = ∫ 0 r A r × 4 π r 2 d r E = A 2 ε 0 Since electric field is constant, we get ∆ V = E × d = A 2 ε 0 × R = A R 2 ε 0

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