Question

Assume the dipole model for earth’s magnetic field B which is given by the vertical component of magnetic field, Bv =$\frac { \mu _ { 0 } } { 4 \pi } \frac { \mathrm {~m} \sin \theta } { \mathrm { r } ^ { 3 } }$where 0 = 90° - latitude as measured from magnetic equator, then the loci of point for which dip angle is ± 45°.

• A. $\tan ^ { - 1 } ( 3 )$
• B. $\tan ^ { - 1 }$ (2)
• C. $\tan ^ { - 1 }$($0.5$)
• D. $\tan ^ { - 1 }$(1)

Answer 1

Answer: (B)

$\tan ^ { - 1 }$ (2)

Answer 2

: Here,

$\mathrm { B } _ { \mathrm { H } } = \frac { \mu _ { 0 } } { 4 \pi } \frac { \mathrm { m } \sin \theta } { \mathrm { r } ^ { 3 } }$

and $\delta = 45 ^ { \circ }$

$\because \tan \delta = \frac { B _ { V } } { B _ { H } }$

Hence, $\tan 45 ^ { \circ } = \frac { 2 \cos \theta } { \sin \theta } = 2 \cot \theta$

$\therefore 1 = \frac { 2 } { \tan \theta } \Rightarrow \tan \theta = 2$

or $\theta = \tan ^ { - 1 }$ (2) is the loci of points.