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  • The earth's magnetic field at a certain place has horizontal component 0.3 gauss and the total strength 0.5 gauss. The angle of dip isOption: 1 <

The earth's magnetic field at a certain place has horizontal component 0.3 gauss and the total strength 0.5 gauss. The angle of dip is

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

As we have learnt,

 

Resultant Magnetic Field due to earth -

B_{H}=B\cos \phi

B_{V}=B\sin \phi

B=\sqrt{B_{H}^{2}+B_{V}^{2}}

-

 

 B^2 = B_V^2 + B_H^2 \Rightarrow B_V = \sqrt{B^2 - B_H^2} = \sqrt{(0.5)^2 - (0.3)^2} = 0.4

Now, Angle of dip =   \tan^{-1}\left( \frac{B_V}{B_H}\right )

 

\tan\phi = \frac{B_V}{B_H} = \frac{0.4}{0.3} = \frac{4}{3} \Rightarrow \phi = \tan^{-1}\left(\frac{4}{3} \right )

 

Posted by

Sumit Saini

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