Question

Consider the Earth as a short magnet with its centre coinciding with the centre of the Earth and dipole moment is $M$. The angle of dip $\delta$ is related to latitude $\lambda$ as :

• A. $\tan \delta =\tan \lambda$
• B. $\tan \delta =2\tan \lambda$
• C. $\tan \delta =\frac{\tan \lambda }{2}$
• D. $\tan \delta =\cot \lambda$

Answer 1

The correct option is B $\tan \delta =2\tan \lambda$

$B_r=\frac{2{\mu }_{0}M}{4\pi r^3}\cos \theta$

$B_{\theta }=\frac{{\mu }_{0}M\sin \theta }{4\pi r^3}$ as $\theta =90+\lambda$

$B_r=\frac{2{\mu }_{0}M}{4\pi r^3}\cos (90+\lambda )=\frac{-2{\mu }_{0}M\sin \lambda }{4\pi r^3}$

$B\theta =\frac{{\mu }_{0}M\sin (90+\lambda )}{4\pi r^3}=\frac{{\mu }_{0}M\cos \lambda }{4\pi r^3}$

$\frac{B_r}{B_{\theta }}=\frac{B_r}{B_{\theta }}=-2\tan \lambda$ or $\tan \delta =2\tan \lambda$