Expression for Inductance - General Physics - Solved Past Paper, Exams of Physics

Download Expression for Inductance - General Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity! 2. (30 pts) A long, straight coaxial cable consists of two concentric cylindrical conductors of radii a and b and length ℓ as shown below. The inner conductor is a thin cylindrical shell. The conductors carry current I in opposite directions. Derive an expression for the inductance of this section of cable. B r a b dr I I a) (10 pts) Work out the expression for the magnetic field in the region of space between the two conductors (i.e. a < r < b). Using Ampere’s Law around the dashed curve of radius r shown in the figure, we have ∮ ~B · dℓ = µ0Ienc 2πr B = µ0I B = µ0I 2πr b) (10 pts) Given the magnetic field from (a), what is the magnetic flux through the shaded rectangular region shown in the figure? Note that the magnetic field magnitude is not constant at all locations in the shaded region. Note that the magnetic field is not uniform in this case, so there are no short-cuts to evaluating the flux integral this time. Φ = ∫∫ ~B · d~a = µ0Iℓ 2π b ∫ a dr r = µ0Iℓ 2π ln ( b a ) c) (10 pts) Finally, considering that a cylindrical shell comprises only one loop, determine the induc- tance of this cable given the current I and your answer to (b). L = NΦ I = µ0Iℓ 2πI ln ( b a ) = µ0ℓ 2π ln ( b a )