A very long solenoid is made out of a wire with n turns per unit length. The radius of the cylinder is a and is negligible compared to its length l . The interior of the cylinder is filled with materi

Question

A very long solenoid is made out of a wire with $n$ turns per unit length. The radius of the cylinder is $a$ and is negligible compared to its length $l$ . The interior of the cylinder is filled with materials such that the linear magnetic permeability varies with the distance $r$ from axis according to
$μ (r) = \{\begin{matrix} μ_{1} = c o n s t a n t; f o r 0 < r < b \\ μ_{2} = c o n s t a n t; f o r b < r < a \end{matrix}\}$
The self-inductance of the solenoid is

TestHub · Accepted Answer

Self-inductance of the solenoid is given by

$L = μ (r) n^{2} π a^{2} l$

Here, $μ$ varies with distance $r$ .

So, the self-inductance can be written as

$L = μ_{1} n^{2} l π b^{2} {|_{0 < r < b} + μ_{2} n^{2} l (π a^{2} - π b^{2})|}_{b < r < a}$

$= π n^{2} l [μ_{1} b^{2} + μ_{2} (a^{2} - b^{2})]$

Physics - EMI/AC Question with Solution | TestHub

Options:

Doubts & Discussion