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Considering the earth as a short magnet ...

Considering the earth as a short magnet with its centre coinciding with the centre of earth, show that the angle of dip `phi` is related to magnetic latitude `lambda` through the relation `tan phi=2 tan lambda`

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Considering the situation as shown in fig.,
For dipole, at position `(r. theta )` we have
`B_(r)=mu_(0)4pi 2Mcos theta/r^(3)`
and`B_(0)=mu_(0)/4pi Msin theta/r^(3)`and as `tan phi=B_(v)/B_(B)=-B_(r)/B_(theta)`
`tan phi=-2 cot theta`
But from fig..,`theta=90^@+lambda`
So,`than phi=-2cot(90^(@)+lambda)`,i.e.,`tan phi=2tan lambda`
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