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Two long coaxial and conducting cylinders of radius a and b are separated by a material of conductivity sigma and a constant potential difference V is maintained between them by a battery. Then the current per unit length of the cylinder flowing from one cylinder to the other is |
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Answer» `(4pisigma)/(LN(b//a))V ` cylinder. And `V = int_ (a)^(b) Edl = lambda/(2piepsilon_0) In (b/a)` Now, `I = int vec(J).d vec(A) = sigma int vec(E ) * d vec (A)` ` = sigma int (lambda/(2piepsilon_0r)) 2pir dr ` Current per unit LENGTH will be `I = (sigmalambda)/(epsilon_0)` From Eq. (i), we get `I = (2sigmapiepsilon_0)/(epsilon_0In (b//a)) v = (2pi sigma)/(In(b//a)) v` Alternatively, `I = V/R or R = int_(x=a)^(b) (i/sigma)(dx)/(2pix 1) = 1/(2pir) In (b/a)` `:.I = (2pisigmaV)/(In (b//a))` . |
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