Question

7. Two wires of the same length are shaped into a square of side 'a' and a circle with radius 'r'. If they carry same current, the ratio of their magnetic moment is 2: TT (0) (ii) (iii) (iv) TT : 2 T : 4 4:TT ​

Answer 1

2:TT(0)(ii) (iii) (iv) TT:2T:4 4:TT

Answer 2

Given info : Two wire of the same length are shaped into a square of side a and a circle with radius r.

To find : if they carry same current , the ratio of  their magnetic moment is...

solution : we know, magnetic moment is given by, m = NiA

where, N is number of turns , i is current through a wire and A is cross section area.

here, N and i remain constant. so magnetic moment is directly proportional to cross sectional area of shaped wire.

for the wire which is shaped into a squre :

length of wire = perimeter of square

⇒ l = 4a

⇒ a = l/4

now the area of square, A₁ = a² = (l/4)² = l²/16

for the wire which is shaped into a circle :

length of wire = circumference of circle

⇒ l = 2πr

⇒ r = l/2π

now the area of circle, A₂ = πr² = π(l/2π)² = l²/4π

now the ratio of their magnetic moment is ..

m₁/m₂ = A₁/A₂

= (l²/16)/(l²/4π)

= π/4

therefore the ratio of their magnetic moment is π : 4.