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)

विकल्प

• `(2B)/mu_0 sqrt (A^3/pi)`

• `(BA^2)/(4 mu_0 pi)`

• `(2 pi)/mu_0 sqrt (A^3)`

• `mu_0/(2B) sqrt (A^3/pi)`

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 `bbunderline((2B)/mu_0 sqrt (A^3/pi))`.

Explanation:

We know,

M = iA and

A = πR²

Also,

B = `(mu_0 i)/(2R)`

∴ i = `(2BR)/(mu_0)`

∴ i = `(2B)/mu_0 xx sqrt(A/pi)`

∴ m = `(2B)/mu_0 sqrt(A/pi) xx A`

= `(2B sqrt(A^3))/(mu_0 sqrt pi)`