Magnetic induction produced at the centre of a circular loop carrying current is B . The magnetic moment of the loop of radius R is
(Me = permeability of tree space)

Options

A. `(BR^(3))/(2pi mu_(0))`
B. `(2 pi BR^(3))/(mu_(0))`
C. `(BR^(2))/(2 pi mu_(0))`
D. `(2pi BR^(2))/(mu_(0))`

Answer

B

Explanation

Magnetic moment
`M = I xx A " " … (i)`
Current `xx` Area of enclosed by loop
Magnetic induction at the centre of circular loop
`B = (mu_(0)I)/(2R) implies I = (2 BR)/(mu_(0))`
Here , `A = pi R^(2) " " … (iii)`
Substituting Eq.(ii)( and Eq.(iii) in Eq.(i) , we get
`M = (2BR)/(mu_(0)) xx pi R^(2) = (2pi BR^(3))/(mu_0)`