Question

A circular coil and a square coil is prepared from two Identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is ______.

पर्याय

• `2/pi`

• `pi/2`

• π

• `4/pi`

Answer 1

A circular coil and a square coil is prepared from two Identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is `underline(4/pi)`.

Explanation:

Let I be the length of metal wire.

When wire is bent into a circular coil of radius r, then

r = `l/(2pi)`

∴ Area, A = `pi(l/(2pi))^2 = pi l^2/(4pi^2)`

∴ Magnetic dipole moment associated with circular coil,

`mu_"c" - "iA" = "i"pi (l^2/(4pi^2))`

`mu_"c" = "il"^2/(4pi)`     ....(i)

When metal wire Is bent into a square coil then side of square

a = `l/4`

∴ Area, A = `"a"^2 = l^2/16`

∴ Magnetic dipole moment associated with square coil,

`mu_"s" = "i A" = "i"  l^2/16`

∴ `mu_"c"/mu_"s" = (("i"l^2)/(4pi))/(("i"l^2)/(16))`

`= 16/(4pi) = 4/pi`

Hence, the ratio of magnetic dipole moment of circular coil and square coil Is 4 : π.