The magnetic field of a planet at any location is approximately 0.5 G. Estimate its dipole moment if its position from the centre is \( 25.6\times10^{6}\,\mathrm{m} \). Assume the planet to be of spherical shape:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 8.39\times10^{24}\,\mathrm{A\,m^{2}} \)
A planet’s field is that of a magnetic dipole. At a distance r from the centre, on the equatorial plane, the field is \( B = \frac{\mu_0}{4\pi}\frac{M}{r^{3}} \), where M is the dipole moment. Taking the given field as this value:
\( B = 0.5\,\mathrm{G} = 0.5\times10^{-4}\,\mathrm{T},\qquad \displaystyle\frac{\mu_0}{4\pi} = 10^{-7}\,\mathrm{T\,m\,A^{-1}} \)
\( \displaystyle M = \frac{B\,r^{3}}{\mu_0/4\pi} = \frac{(0.5\times10^{-4})(25.6\times10^{6})^{3}}{10^{-7}} \)
\( \displaystyle M = \frac{0.5\times10^{-4}\times1.678\times10^{22}}{10^{-7}} = 8.39\times10^{24}\,\mathrm{A\,m^{2}} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
The Earth’s Magnetism – “… Example 5.8 The earth’s magnetic field at the equator is approximately 0.4 G. Estimate the earth’s dipole moment.”