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:

Options

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

Answer

C

Explanation

Initially, dipole moment of circular loop is `m=I.A=I.piR^(2)` and magnetic field `B_(1)=(mu_(0)I)/(2R)`
Finally, dipole moment becomes double, keeping current constant, so radius of the loop becomes `sqrt(2)R`.
`B_(2)=(mu_(0)I)/(2(sqrt(2R)))=(B_(1))/(sqrt(2)), :. (B_(1))/(B_(2))=sqrt(2)`