Question

If \(F\) represents the Earth's total magnetic field corresponding to its dipole source only, then the increase in \(F\) from 0\(^\circ\) to 60\(^\circ\) N magnetic latitude is __________ % (rounded off to one decimal place).

Hint:

Use the geocentric dipole field formula \(F(\lambda) = F_0\sqrt{1+3\sin^2\lambda}\) and compare its values at 0 and 60 degrees.

Answer 1

Correct Answer: 80

For a pure geocentric dipole, the total field magnitude at magnetic latitude \(\lambda\) is \(F(\lambda) = F_0\sqrt{1 + 3\sin^2\lambda}\), where \(F_0\) is the field magnitude at the magnetic equator (\(\lambda=0\)).

Step 1: Field at the equator.
At \(\lambda = 0^\circ\): \(F(0) = F_0\).

Step 2: Field at 60\(^\circ\)N.
\(F(60^\circ) = F_0\sqrt{1 + 3\sin^2 60^\circ} = F_0\sqrt{1 + 3(0.75)} = F_0\sqrt{3.25} = 1.8028\,F_0\).

Step 3: Percentage increase.
\(\dfrac{F(60^\circ)-F(0)}{F(0)}\times100 = (1.8028-1)\times100 = 80.28\%\).

Rounded to one decimal place, the increase is \(\boxed{80.3\%}\), inside the accepted band 80.0 to 80.5%.