A conducting sphere with inner radius R and outer radius 3R has some alloys mixed in it due to which its resistivity changes with radial distance r according to the function ρ r = Kr , where K is a

Question

A conducting sphere with inner radius R and outer radius 3R has some alloys mixed in it due to which its resistivity changes with radial distance r according to the function $ρ_{r} = Kr$ , where K is a +ve constant. Inner surface of the sphere is grounded while outer surface of sphere is maintained at potential $V_{0}$ with the help of a battery of emf $V_{0}$ . Battery is ideal. What will be the potential of the sphere at radial distance of 2R

TestHub · Accepted Answer

A thin spherical shell has resistance: d R = 4 π r 2 Kr d r ​ = 4 π K ​ r d r ​ R R → 3 R ​ = 4 π K ​ ln 3 The same radial current passes through every shell. V ( 2 R ) = V 0 ​ R R → 3 R ​ R R → 2 R ​ ​ = V 0 ​ l n 3 l n 2 ​ Answer A.

Physics - Current Electricity Question with Solution | TestHub

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