Question

Two wire of same length are shaped into a square and a circle. If they carry same current, ratio of magnetic moment is

Answer 1

Answer: (c) π : 4

Let length of wire is ℓ.

hence side of square = (ℓ/4)

area of square be (ℓ/4)2 = (ℓ2 / 16) (1)

radius of circle = r = (ℓ / 2π)

area of circle = πr2 = (πℓ2 / 4π2) = (ℓ2 / 4π) (2)

Let magnetic moment of square is μ1 and circle is μ2.

hence μ1 = I1A1 & μ2 = I2A2

if current is same i.e. I1 = I2 then

(μ1 / μ2) = (A1 / A2) = [(ℓ2 / 16) / (ℓ2 / 4π)]

= (4π / 16) = (π/4) from (1) & (2)