A) \[\frac{\alpha }{4\pi (b+a)}\]
B) \[\frac{\alpha }{4\pi }\left( \frac{1}{b}-\frac{1}{a} \right)\]
C) \[\frac{\alpha }{4\pi }\left( \frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}} \right)\]
D) \[\frac{\alpha }{4\pi }\left( \frac{1}{a}-\frac{1}{b} \right)\]
E) \[\frac{\alpha }{4\pi (b-a)}\]
Correct Answer: D
Solution :
Caisider a concentric spherical shell of radius \[x\] and thickness \[dx\] as showing in figure, its resistance is\[{{d}_{R}}=\frac{\rho \,dx}{4\pi {{x}^{2}}}\] \[\therefore \]Total resistance \[R=\frac{\rho }{4\pi }\int_{a}^{b}{\frac{dx}{{{x}^{2}}}}\] \[=\frac{\rho }{4\pi }\left[ \frac{1}{a}-\frac{1}{b} \right]\]You need to login to perform this action.
You will be redirected in
3 sec