Magnetic field at the centre of a circualr loop of area A carrying current I is B. What is the magnetic moment of this loop?

Options

A. `((BA)^(2))/(mu_(0)pi)`
B. `(BAsqrtA)/(mu_(0))`
C. `(BA sqrtA)/(mu_(0)pi)`
D. `(2BAsqrtA)/(mu_(0)sqrtpi)`

Answer

D

Explanation

Let r be the radius of the circular loop.
`therefore" "A=pir^(2) or r=sqrt((A)/(pi))`
Magnetic field at the centre of the loop is
`B=(mu_(0)I)/(2r)=(mu_(0)I)/(2sqrt((A)/(pi)))orI=(2B)/(mu_(0))sqrt((A)/(pi))`
The magnetic moment of the loop is
`M=IA=(2B)/(mu_(0))sqrt((A)/(pi))A=(2BAsqrtA)/(mu_(0)sqrtpi)`