A dip needle lies initially in the magnetic meridian when it...

A dip needle lies initially in the magnetic meridian when it shows an angle of dip at a place. The dip circle is rotted through an angle $\mathrm{x}$ in the horizontal plane and then it shows an angle of dip $\theta^{\prime}$. Then $\left[\left(\tan \theta^{\prime}\right) /(\tan \theta)\right]$ is (a) $[1 /(\cos x)]$ (b) $[1 /(\sin x)]$ (c) $[1 /(\tan \mathrm{x})]$ (d) $\cos \mathrm{x}$

A dip needle lies initially in the magnetic meridian when it shows an angle of dip at a place. The dip circle is rotted through an angle $\mathrm{x}$ in the horizontal plane and then it shows an angle of dip $\theta^{\prime}$. Then $\left[\left(\tan \theta^{\prime}\right) /(\tan \theta)\right]$ is
(a) $[1 /(\cos x)]$
(b) $[1 /(\sin x)]$
(c) $[1 /(\tan \mathrm{x})]$
(d) $\cos \mathrm{x}$

Key Concepts

Magnetic Dip Angle

The magnetic dip angle (or inclination) is the angle made by the Earth’s magnetic field with the horizontal plane. It is a fundamental parameter in geomagnetism and is measured using instruments like the dip needle. Understanding the dip angle is essential for studying how the Earth's magnetic field varies spatially.

Dip Needle and Dip Circle Instrument

A dip needle, often mounted on a dip circle, is an instrument used to measure the magnetic dip angle. It aligns itself along the direction of the Earth's magnetic field and the dip circle allows for rotation of the needle through different azimuths, revealing how the observed dip angle changes as the instrument is oriented away from the magnetic meridian.

Rotation and Projection of Vector Components

When the dip circle is rotated in the horizontal plane by an angle, the measured dip angle changes due to the projection of the magnetic field vector onto the new plane of measurement. The relationship between the new dip angle and the original one is determined by resolving the components of the magnetic field, highlighting the effect of instrument orientation in vector measurements.

Trigonometric Relationships in Magnetic Field Measurements

The analysis of how the measured dip angle changes with rotation involves trigonometric functions. In this context, the ratio of tangents of the dip angles before and after rotation is expressed in terms of the cosine of the rotation angle. This relation stems from the fundamental trigonometric identities that relate the projection of a vector into rotated coordinate systems.

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