Question

A current carrying wire of length l is bent to form a circular coil of one turn . after that it is again bent to form a circular coil of two turns. find ratio of magnetic moment of coils respectivly.

Answer 1

ratio of magnetic moment of coils is 2 : 1.

case 1 : A current carry wire of length l is bent to form a circular coil of one turn.

i.e., Number of turns, N = 1

radius , r = l/2π

and area, A = πr² = πl²/4π² = l²/4π

now magnetic moment, m = ANI

= l²/4π × 1 × i

= l²i/4π ..........(2)

case 2 : after that it is again bent to form a circular coil of two turns.

so, number of turns , N' = 2

radius of coil, r' = l/4π

and area, A' = πr'² = π × l²/16π² = l²/16π

now magnetic moment, m' = A'N'i

= l²/16π × 2 × i

= l²i/8π ........(2)

from equations (1) and (2) we get,

m/m' = 2/1

hence, ratio of magnetic moment of coils is 2 : 1

Answer 2

$\huge\bold\purple{Answer:-}$

case 1 : A current carry wire of length l is bent to form a circular coil of one turn.

i.e., Number of turns, N = 1

radius , r = l/2π

and area, A = πr² = πl²/4π² = l²/4π

now magnetic moment, m = ANI

= l²/4π × 1 × i

= l²i/4π ..........(2)

case 2 : after that it is again bent to form a circular coil of two turns.

so, number of turns , N' = 2

radius of coil, r' = l/4π

and area, A' = πr'² = π × l²/16π² = l²/16π

now magnetic moment, m' = A'N'i

= l²/16π × 2 × i

= l²i/8π ........(2)

from equations (1) and (2) we get,

m/m' = 2/1

hence, ratio of magnetic moment of coils is 2 : 1