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,

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

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