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Physics Question on the earth's magnetic field

The angle of dip at a place is 37o{{37}^{o}} and the vertical component of the earths magnetic field is 6×10−5T.6\times {{10}^{-5}}T. The earths magnetic field at this place is (tan 37o=3/4)(tan\text{ }{{37}^{o}}=3/4)

A

7×10−5T7\times {{10}^{-5}}T

B

6×10−5T6\times {{10}^{-5}}T

C

5×10−5T5\times {{10}^{-5}}T

D

10×10−4T10\times {{10}^{-4}}T

Answer

10×10−4T10\times {{10}^{-4}}T

Explanation

Solution

Given: tan⁡37o=34\tan {{37}^{o}}=\frac{3}{4}
The vertical component of the earths magnetic field
BV=6×10−5T{{B}_{V}}=6\times {{10}^{-5}}T
sin⁡37o=35\sin {{37}^{o}}=\frac{3}{5}
For vertical component BV=Bsin⁡θ{{B}_{V}}=B\sin \theta
Or B=BVsin⁡θB=\frac{{{B}_{V}}}{\sin \theta }
Or B=6×10−53×5B=\frac{6\times {{10}^{-5}}}{3}\times 5
Or B=10×10−5B=10\times {{10}^{-5}}
Or B=10−4TB={{10}^{-4}}T