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Space between tow concentric spheres of ...

Space between tow concentric spheres of radii `r_(1) and r_(2)` such that `r_(1) lt r_(2)` is filled with a material of resistivity `rho`. Find the resistance between inner and outer surface of the material

A

`(r_(1))/(r_(2))(p)/(2)`

B

`(r_(2)-r_(1))/(r_(1)r_(2))(p)/(4pi)`

C

`(r_(1)r_(2))/(r_(2)-r_(1))(p)/(4pi)`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `R=rho(l)/(a) therefore R=rho=(dl)/(4pil^(2))` (where l is any radius and dl is small element).
`R=(rho)/(4pi) underset(r_(1))overset(r_(2))(int)(dl)/(l^(2))=(rho)/(4pi)[-(1)/(l)]_(r_(1))^(r_(2))=(rho)/(4pi)[(1)/(r_(1))-(1)/(r_(2))]`
`R=[(r_(2)-r_(1))/(r_(1)r_(2))](rho)/(4pi)`
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