Question

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 ______.

Options

• 2 : π

• π : 2

• π : 4

• 4 : π

Answer 1

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 π : 4.

Explanation:

l = length of wire

 

Area of a Square = a2 Also here l = 4a a = `1/4` `therefore "Area" = 1^2/16` `"A"_1 = 1^2/16`

Area of a Circle = πr2 Also here, 2πr = 1 r = `1/(2pi)` Now Area = `pi(1/(2pi))^2` `"A"_2 = 1^2/(4pi)`

Now Magnetic moment = I A

∴ M₁ = IA, & M₂ = I A₂

Since I (current) is same in both

`∴ "M"_1/"M"_2 = "A"_1/"A"_2`

`= 1^2/16 = (4pi)/1^2 = pi/4`

M₁ M₂ = π : 4