You are given a length (l) of wire that has radius (a)and are told to wind it into an inductor in the shape of a helix that has a circular cross section of radius (r). the windings are to be as close together as possible without overlapping. show that the self-inductance of this inductor is l = 1/4nrl/a.

To solve this problem it is necessary to apply the concepts related to inductance on an inductor, which is mathematically described as:

Where,

= Permeability constant (Described as 'n' at the problem equation)

l = Length

A = Cross-sectional Area

n = No of turn per unit length

The number of turns N is given by

The number of turns per unit length n is

The relationship of the cable lengths starts from assuming that the length 'a' is less than the length 'r', and therefore the length of the wire d would be related by:

Solving to obtain l,

Substituting at the first equation,

they start with the same

the answer is to check all of them! they all apply well at least i think so!