Two long coaxial and conducting cylinders of radius a and b are separated by a material of conductivity σ and a constant potential difference V is maintained between them, by a battery. Then the curre

Question

Two long coaxial and conducting cylinders of radius a and b are separated by a material of conductivity σ 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 -

TestHub · Accepted Answer

V = ∫ a b ​ E ⋅ d ℓ = 2 π ε 0 ​ r λ ​ ln ( a b ​ ) Now, I = σ ∫ E ⋅ d A = σ ∫ 2 π ε 0 ​ r λ ​ ⋅ 2 π d r = ε 0 ​ σλ ​ From (1) : I = ε 0 ​ l n ( b / a ) 2 σπ ε 0 ​ ​ = l n ( b / a ) 2 πσ ​ v

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