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 made three times by keeping the current I same, the magnetic field at the centre of the loop becomes \( B_2 \). The ratio of \( B_1 \) and \( B_2 \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sqrt{3} : 1 \)
The magnetic dipole moment of a loop is \( m = I\pi R^{2} \), and the field at its centre is \( B = \mu_0 I/(2R) \). With \( I \) fixed, \( m \propto R^{2} \) and \( B \propto 1/R \).
\( \displaystyle m_2 = 3m_1 \;\Rightarrow\; R_2^{2} = 3R_1^{2} \;\Rightarrow\; R_2 = \sqrt{3}\,R_1 \)
\( \displaystyle \frac{B_1}{B_2} = \frac{R_2}{R_1} = \sqrt{3} : 1 \)