question_answer

Space between two concentric conducting spheres of radii a and \[b\left( b>a \right)\] is filled with a medium of resistivity\[\rho \]. The resistance between the two spheres will be : [JEE Main 10-4-2019 Afternoon]

A) \[\frac{\rho }{4\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]    

B) \[\frac{\rho }{2\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]

C) \[\frac{\rho }{2\pi }\left( \frac{1}{a}+\frac{1}{b} \right)\]              

D) \[\frac{\rho }{4\pi }\left( \frac{1}{a}+\frac{1}{b} \right)\]

Correct Answer: A

Solution :

\[dR=\rho .\frac{dx}{4\pi {{x}^{2}}}\]           \[\int_{{}}^{{}}{dR}=\rho .\int\limits_{a}^{b}{\frac{dx}{4\pi {{x}^{2}}}}\]           \[R=\frac{\rho }{4\pi }\left[ -\frac{1}{x} \right]_{a}^{b}\]           \[R=\frac{\rho }{4\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]