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. `sqrt2`
B. `1/sqrt2`
C. `2`
D. `sqrt3`.

Answer

a

Explanation

Dipole moment is defined as current multiplied with area which is `pi r^(2)` for the circular loop. Keeping current constant, dipole moment can be changed by changing radius of the loop. We can write magnetic field and dipole moment in the given two cases as follows:
`beta_(1) = (mu_(0)I)/(2r_(1)) " and " m_(1) = I (pi r_(1)^(2))`
`beta_(2) = (mu_(0)I)/(2r_(2)) " and " m_(2) = I (pi r_(2)^(2))`
` m_(2)/m_(1) = 2 rArr r_(2)^(2)/r_(1)^(2) = 2 rArr r_(2)/r_(1) = sqrt2`
`B_(1)/B_(2) = r_(2)/r_(1) = sqrt2`
hence option (a) is correct.