A long solonoid carrying a current produces a magnetic field along its axis. If the current is doubled and the number of turns per cm is halved, the new value of the magnetic field is

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.