NTA Abhyas JEE Main2020PhysicsElectrostaticsPractice
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
Options
- AA R 8 ε 0
- BA R 4 ε 0
- CA R ε 0
- DA R 2 ε 0
Correct answer
D. A R 2 ε 0
Step-by-step solution
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