AP EAMCET · PHYSICS · Magnetic Properties of Matter

The plane of a dip circle is set in the geographic meridian and the apparent dip is $δ_{1}$ . It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is $δ_{2}$ . The declination $θ$ at the place is

A $\tan^{- 1} (\tan δ_{1} \tan δ_{2})$
B $\tan^{- 1} (\tan δ_{1} + \tan δ_{2})$
C $\tan^{- 1} (\frac{\tan δ_{1}}{\tan δ_{2}})$
D $\tan^{- 1} (\tan δ_{1} - \tan δ_{2})$

Verified Solution

Answer & Solution

Correct Answer

(C) $\tan^{- 1} (\frac{\tan δ_{1}}{\tan δ_{2}})$

Step-by-step Solution

Detailed explanation

Apparent dip angle if the plane of a dip circle is set in the geographic meridian, tanδ1=tanϕcosα⇒cosα=tanϕtanδ1 ⋯1 Apparent dip angle if the vertical plane perpendicular to the geographic meridian,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The plane of a dip circle is set in the geographic meridian and the apparent dip is δ1. It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is δ2. The declination θ at the place is

Step-by-step Solution

The plane of a dip circle is set in the geographic meridian and the apparent dip is $δ_{1}$ . It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is $δ_{2}$ . The declination $θ$ at the place is