Question

A square loop and a circular loop are formed from the same wire and the same current is passed through them. The ratio of their dipole moments is ______.

Options

• 4π

• π

• 1

• π/4

Answer 1

A square loop and a circular loop are formed from the same wire and the same current is passed through them. The ratio of their dipole moments is π/4.

Explanation:

Dipole moment P = IA

where, I = current flowing through the wire of loop and A = area

Let length of the wire be L

`therefore ("P"_("Civ loop"))/("P"_("sq loop")) = ("I"pi"R"^2)/("I" l^2)`

`= (pi "L"^2/(4pi^2))/("L"^2/16)`   ...(∵ 2πR = L and for square l = L/4)

`= (pi"L"^2)/(4pi^2) xx 16/"L"^2 = 4/pi`

or, `("P"_("Civ loop"))/("P"_("sq loop")) = pi/4`