A charge is uniformly distributed inside a spherical body of radius r 1 = 2 r 0 having a concentric cavity of radius r 2 = r 0 ( ρ is charge density inside the sphere). The potential of a point P at a distance 3 r 0 2 from the centre is

Question

A charge is uniformly distributed inside a spherical body of radius r 1 = 2 r 0 having a concentric cavity of radius r 2 = r 0 ( ρ is charge density inside the sphere). The potential of a point P at a distance 3 r 0 2 from the centre is, 7 ρ r 0 2 6 ε 0, 101 ρ r 0 2 72 ε 0, 17 ρ r 0 2 72 ε 0, none of these

MARKS App · Accepted Answer

Electric field at a distance r , r 0 r 2 r 0 from the center is given by, E = 1 4 πε 0 . q enclosed r 2 = 1 4 πε 0 . ρ . 4 3 π ( r 3 − r 0 3 ) r 2 = ρ 3 ε 0 . ( r − r 0 3 r 2 ) Potential at the outer surface, V s = 1 4 πε 0 . Q 2 r 0 = 1 4 πε 0 . ρ . 4 3 π ( ( 2 r 0 ) 3 - r 0 3 ) 2 r 0 = 7 ρ 6 ε 0 . r 0 2 ∴ If V is the required potential at r = 3 r 0 2 , V − V s = − ∫ 2 r 0 3 r 0 2 E . dr V = V s − ρ 3 ε 0 ∫ 2 r 0 3 r 0 2 ( r − r 0 3 r 2 ) dr = 7 ρ 6 ε 0 r 0 2 − ρ 3 ε 0 ( r 2 2 + r 0 3 r ) | 2 r 0 3 r 0 2 = 7 ρ 6 ε 0 r 0 2 − ρ 3 ε 0 [ 1 2 ( 9 x 0 2 4 − 4 r 0 2 ) − ( 2 r 0 3 3 r 0 − r 0 3 2 r 0 ) ] = 101 ρr 0 3 72 ε 0

Search any question & find its solution

Looking for more such questions to practice?