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

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 (A)  tan -1 (3/4) (B)  sin -1 (3/4) (C)  tan -1 (4/3) (D)  sin -1 (3/5)

Tardigrade Admin · Accepted Answer

B2=BV2+BH2 ⇒ BV=√B2-BH2=√(0.5)2-(0.3)2 =0.4 Now, tan φ=(BV/BH)=(0.4/0.3)=(4/3) ⇒ φ= tan -1((4/3))

Q. 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

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

$sin^{- 1} \frac{3}{4}$

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

$sin^{- 1} \frac{3}{5}$

$B^{2} = B_{V}^{2} + B_{H}^{2}$
$\Rightarrow B_{V} = B^{2} - B_{H}^{2} = (0.5)^{2} - (0.3)^{2}$
$= 0.4$
Now, $tan ϕ = \frac{B _{V}}{B _{H}} = \frac{0.4}{0.3} = \frac{4}{3}$
$\Rightarrow ϕ = tan^{- 1} (\frac{4}{3})$

Q. 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−143​

sin−143​

tan−134​

sin−153​