The magnetic moment of a current loop is \( 2.1\times10^{-25}\,\mathrm{A\,m^{2}} \). The magnetic field on the axis of the loop at a distance of 1.0 Å from the loop would be: (Given radius of loop negligible)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 4.2\times10^{-2}\,\mathrm{T} \)
At a distance r much larger than its radius, a current loop of magnetic moment m behaves like a magnetic dipole, and its field on the axis is:
\( \displaystyle B = \frac{\mu_0}{4\pi}\,\frac{2m}{r^{3}} \)
Here \( \mu_0/4\pi = 10^{-7}\,\mathrm{T\,m\,A^{-1}} \) and \( r = 1.0\,\mathrm{\mathring{A}} = 10^{-10}\,\mathrm{m} \).
\( \displaystyle B = 10^{-7}\times\frac{2\times2.1\times10^{-25}}{(10^{-10})^{3}} = 10^{-7}\times\frac{4.2\times10^{-25}}{10^{-30}} \)
\( B = 10^{-7}\times4.2\times10^{5} = 4.2\times10^{-2}\,\mathrm{T} \)