Assume the dipole model of earth's magnetic field B which is given by `B_V`= vertical component of magnetic field `=(mu_0)/(4pi)(2Mcos theta)/(r^3)`, `B_H`=Horizontal component of magnetic field `=(mu_0)/(4pi)(sin theta M)/(r^3)`, `theta=90^@`-latitude as measured from magnetic equator.
Find loci of points for which (i) `|vecB|` is minimum, (ii) dip angle is zero, and (iii) dip angle is `+-45^@`.

Options

A. `tan^(-1)(3)`
B. `tan^(-1)(2)`
C. `tan^(-1)(0.5)`
D. `tan^(-1)(1)`

Answer

B

Explanation

Here, `B_(V)=(mu_(0))/(4pi)(2m cos theta)/(r^(3))`
`B_(H)=(mu_(0))/(4pi)(m sin theta)/(r^(3))and delta=45^(@)`
`therefore tan delta=(B_(V))/(B_(H))`
Hence, `tan 45^(@)=(2 cos theta)/(sin theta)= 2 cot theta`
`therefore 1=(2)/(tan theta) Rightarrow tan theta=2`
`or theta=tan^(-1)(2) "is the loci of points"`