A coil of n turns and radius r is carrying current i If radius is made r/4 and it - Physics -

Question

A coil of n turns and radius r is carrying current i If radius is
made r/4 and it carries current i what will be the ratio of
magnetic moments? ( this is a mhcet question so I wanted to know
why the number of turns becomes 4n in the second case? )

Vaibhav T. · Accepted Answer

Dear Student,

The expression for magnetic moment of a current carrying coil ism=niAwhere, n=number of turnsi=current flowing in coilA=area of cross sectionn×2πr=n'×2π×r4n'=4nNow, area of circular coil, A=πr2m1=niπr2If r=r4 then,m2=n'iπr42m2=π4nir216m2=niπr24m1m2=niπr2niπr24m1m2=41

A coil of n turns and radius r is carrying current i. If radius is made r/4 and it carries current i what will be the ratio of magnetic moments? ( this is a mhcet question so I wanted to know why the number of turns becomes 4n in the second case? )