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

Options

A. `sqrt(2)`
B. `(1)/(sqrt(2))`
C. 2
D. `sqrt(3)`

Answer

A

Explanation

We , know , dipole moment , m = IA
[ I is loop current , A is area of the loop ]
`thereforem = IxxpiR^(2)` [ R is the radius of the loop ]
According to the question , in the second case dipole moment ,
`m'=2m=Ixxpi(sqrt(2))`
`therefore` In the second case the radius of the loop will be `sqrt(2R)` .
Now , `(B_(1))/(B_(2))=((mu_(0)I)/(2R))/((mu_(0)I)/(2xxsqrt(2R)))=sqrt(2)`