Space between two concentric conducting spheres of radii a and b ( b > a ) is filled with a medium of…

Space between two concentric conducting spheres of radii a and b (b>a) is filled with a medium of resistivity  ρ . The resistance between the two spheres will be:
  1. ρ4π1a+1b
  2. ρ2π1a+1b
  3. ρ4π1a-1b
  4. ρ2π1a-1b

Solution

Consider small volume element between r and r+dr
Resistance of this volume along rational directions,
dR=ρdr4πr2
As all element resistance are in series,
R=r=ar=bρdr4πr2=ρ4π-1rr=ar=b=ρ4π1a-1b

Asked in: JEE Main 2019 (10 Apr Shift 2)

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