Question

The magnetic field at the centre of a current-carrying circular coil of area A is B. The magnetic moment of the coil is ______.

[µ₀ = permeability of free space]

Options

• `(BA^2)/(mu_0pi)`

• `(2BA^{3"/"2})/(mu_0pi^{1"/"2})`

• `(BA^{3"/"2})/(mu_0pi)`

• `(mu_0pi^{1"/"2})/(BA^{3"/"2})`

Answer 1

The magnetic field at the centre of a current-carrying circular coil of area A is B. The magnetic moment of the coil is `underlinebb((2BA^{3"/"2})/(mu_0pi^{1"/"2}))`.

Explanation:

The magnetic field at the centre of a current-carrying circular coil is given by,

B = `(mu_0i)/(2r)` .......(i)

Also, the area of the coil, A = πr²

⇒ `r = sqrt(A/pi)`

Putting this in Eq. (i), we get,

B = `(mu_0isqrtpi)/(2sqrtA) ⇒ i = (2BsqrtA)/(mu_0sqrtpi)`

The magnetic moment of the coil is given by,

M = NiA = `(2BsqrtA)/(mu_0sqrtpi) xx A`   (∵ N = 1)

= `(2BA^{3"/"2})/(mu_0pi^{1"/"2})`