Question

The earth’s magnetic field at a certain place has a horizontal component 0.3 gauss and the total strength 0.5 gauss. The angle of dip is ${\tan }^{-1}\left(\frac{x}{y}\right)$. Find (x+y).

Answer 1

$B_H$ = horizontal component of earth’s field
$B_V$ = vertical component earth’s field
$\varphi$ = angle of dip
If B is total magnetic field intensity

$B^2=B_V^2+B_H^2$

$B_V=\sqrt{B^2-B_H^2}$

$=\sqrt{(0.5gauss{)}^2-(0.3gauss{)}^2}$

= 0.4 gauss

$\tan \varphi =\frac{B_V}{B_H}$

$=\frac{0.4gauss}{0.3gauss}$

$=\frac{4}{3}$

$\varphi ={\tan }^{-1}\frac{4}{3}$

comparing with ${\tan }^{-1}\left(\frac{x}{y}\right)$

x = 4, y = 3
x + y = 7