Magnetic field at the centre of a circular loop of area A is B. Then the magnetic moment of the loop is
`(mu_(0)` -permeability of the free space)

Options

A. `(BA^(2))/(mu_(0) pi)`
B. `(Basqrt(A))/(mu_(0))`
C. `(Basqrt(A))/(mu_(0)pi)`
D. `(2BAsqrt(A))/(mu_(0)sqrt(pi))`

Answer

D

Explanation

As we know, the magnetic field due to a current carrying circular loop at the centre,
`B = (mu_(0) i)/(2R)` …(i)
So, the magnetic moment of the loop,
`M = iA`
From Eq. (i), we get
`M = (2BR)/(mu_(0)).A`
`because A = pi R^(2)`
`rArr R = sqrt((A)/(pi))`
Hence, `M = (2BAsqrt(A))/(mu sqrt(pi))`
Hence, the correct option is (d).