# How should the diameter of the wire used be chosen so to minimize the heat dissipated in windings ? Check the details in question.

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The turns of a solenoid is designed to provide a given magnetic flux density along its axis are wound to fill the space between 2 concentric cylinder of fixed radii.How should the diameter of the wire used be chosen so to minimize the heat dissipated in windings ?

The turns of a solenoid is designed to provide a given magnetic flux density along its axis are wound to fill the space between 2 concentric cylinder of fixed radii.How should the diameter of the wire used be chosen so to minimize the heat dissipated in windings ?

##### 1 Answer

This is what I get.

#### Explanation:

We are required to fill the cross sectional area between between two concentric cylinders of fixed radii with wire of diameter

Cross section of wire

Resistance of one turn of wire

#Rpropd^-4# .......(2)

We know that magnetic flux density produced

From (1) above becomes

#Ipropd^2# .....(3)

Heat dissipated in a resistance

Using (2) and (3)

Heat dissipated in a resistance

#=># Heat dissipated in a multilayered solenoid, as described above, is independent of diameter of wire.