The magnetic moment of a small current carrying circular loop is 4.0 x 10−2 Am2. The magnetic field on the axis of the loop at a distance of 2 m from the centre of the loop will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 nT
A small current loop behaves as a magnetic dipole. At a distance r much greater than its radius, the field on its axis is
\( \displaystyle B = \frac{\mu_0}{4\pi}\,\frac{2m}{r^{3}} \)
Substituting \( \mu_0/4\pi = 10^{-7}\,\mathrm{T\,m\,A^{-1}} \), \( m = 4.0\times10^{-2}\,\mathrm{A\,m^{2}} \), \( r = 2\,\mathrm{m} \):
\( \displaystyle B = 10^{-7} \times \frac{2 \times 4.0\times10^{-2}}{(2)^{3}}\,\mathrm{T} \)
\( \displaystyle B = 10^{-9}\,\mathrm{T} = 1\,\mathrm{nT} \)