The turns of solenoid, designed to provide a given magnetic fulx density along its axis, are wound to fill the space between two concentric cylinder of fixed radii.How should the diameter d of the wire used be chosen so as to minimize the heat dissipated in the winding?

Options

A. Wire should be multiple of 5d
B. Wire should be multiple of `d//3`
C. Wire is independent of d
D. Can 't say

Answer

C

Explanation

The cross sectional area of the space to be filled is fiexd withlist that of the wire varies as `d^(2)` Thus `nprop d^(-2)` . The resistacne of one turn is inversely proportional to the cross sectional area of the wire i.e varies as `d^(-2)` and hence the resistance per unit length of the solenoid is `Rpropnd^(-2)propd^(-4)` The flux density `Bis prop nI` and therefore the required current `Ipropn^(-1)propd^(2)` The heat dissipated per unit length is `RI^(2)`, Which `propd^(-4)(d^(2)^(2))` i.e independent of chosen so far as the heatin effect is concerned.