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

Answer

A

Explanation

Since , magnetic field at the centre of loop
`B = (mu_(0)I)/(2r)`
`B_(1)=(mu_(0)I)/(2r_(1)),m_(1)=I(pir_(1)^(2))`
`B_(2)=(mu_(0)I)/(2r_(2)),m_(2)=I(pir_(2)^(2))`
`(m_(1))/(m_(2))=(r_(2)^(2))/(r_(1)^(2))rArr 2 = ((r_(2))/r_(1))^(2)rArr (r_(2))/(r_(1))=sqrt(2)`
` :." " (B_(1))/(B_(2)) =sqrt(2)`