GATE 2020 PH – Question 28
Far from Earth its magnetic field is approximated by a bar magnet of magnetic pole strength $4\times10^{14}$ A m. Suppose a current loop around the magnetic equator generates this field. Earth’s circumference is $4\times10^7$ m. The current is approximately $4\times10^n$ A, with integer n. Find n.
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Correct answer: 7 to 7
Explanation
Treat the bar-magnet pole separation as Earth’s diameter 2R. Its dipole moment is $m_d=q_m(2R)$. A circular current loop has moment $I\pi R^2$. Equating moments gives $I=2q_m/(\pi R)=4q_m/C$, where C is the circumference. Thus $I=4(4\times10^{14})/(4\times10^7)=4\times10^7$ A, giving n = 7. Pole strength in A m must not be confused with dipole moment in A m².