JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Current Electricity

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

Answer: (D)

Solution

Imagine the current leaking radially outward through thin spherical shells. A shell of radius

x

and thickness

d x

offers resistance

d R = \frac{ρ d x}{4 π x ^{2}}

, since

4 π x^{2}

is its area. Adding these in series from

a

b

R = \int_{a}^{b} \frac{ρ d x}{4 π x ^{2}} = \frac{ρ}{4 π} [- \frac{1}{x}]_{a}^{b} = \frac{ρ}{4 π} (\frac{1}{a} - \frac{1}{b})

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option