The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is `B_(1)` . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is ` B_(2)` . The ratio `(B_(1))/(B_(2))` is:

Explanation

Magnetic field at the centre of loop `B_(1)=(mu_(0)I)/(2R)`
Dipole moment of circular loop is `m=IA`
`m_(1)=I.A=I.piR^(2)` {R=Radius of the loop}
If moment is doubled (keeping current constant)
R becomeds `sqrt(2R)`
`m_(2)=I.pi(sqrt(2)R)^(2)=2.IpiR^(2)=2m_(1)`
`B_(2)=(mu_(0)I)/(2(sqrt(2)R))`
`:.(B_(1))/(B_(2))=((mu_(0)I)/(2R))/((mu_(0)I)/(2(sqrt(2)R)))=sqrt(2)`