devarshi-dt-logo

Question:

The dipole moment of a circular loop carrying a current I is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B2. The ratio B1/B2 is?

1/√2

√2

√3

2

Solution:

The correct option is A (√2)
Dipole moment M = IA = I(πR²) => R = √(M/Iπ)
Magnetic field at the center Bc = μ₀I/2R
We get Bc = μ₀I/(2√(M/Iπ)) => B ∝ 1/√M => B1/B2 = √(M2/M1) = √(2/1) = √2