Question

Find inductance, L, of a concentric cable composed of two cylindrical wires: a solid inner wire of a radius a = 2 mm carrying a constant current I, and a very thin cylindrical outer wire of a radius b = 5 mm and carrying a constant current ??I.

Answer 1

A solid inner wire of radius 'a' = 2 mm carrying a constant current 'I' and a very thin cylindrical outer wire of radius 'b' = 5 mm carrying a constant current 'I'

From an ampere's law, we have

B = ₀ I / 2x

We know that, d = B dA

d = (₀ I / 2x) (L dx)

integrating on both sides & we have

= (₀ I / 2x) (L dx)

= (₀ I L / 2) (1/x) dx

= (₀ I L / 2) [log (b) - log (a)]

= (₀ I L / 2) ln (b / a)

Therefore, an inductance of a concentric cable will be given as -

L I = (₀ I L / 2) ln (b / a)

L = (₀ L / 2) ln (b / a)