The real angle of dip, if a magnet is suspended at an angle of 30^∘ to the magnetic meridian and

step 1 Hello students in this question we have to calculate the real angle of dip that is theta if the

The real angle of dip, if a magnet is suspended at an angle...

The real angle of dip, if a magnet is suspended at an angle of $30^{\circ}$ to the magnetic meridian and the dip needle makes an angle of $45^{\circ}$ with horizontal, is : (a) $\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ (b) $\tan ^{-1}(\sqrt{3})$ (c) $\tan ^{-1}\left(\frac{\sqrt{3}}{\sqrt{2}}\right)$ (d) $\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$

The real angle of dip, if a magnet is suspended at an angle of $30^{\circ}$ to the magnetic meridian and the dip needle makes an angle of $45^{\circ}$ with horizontal, is :
(a) $\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
(b) $\tan ^{-1}(\sqrt{3})$
(c) $\tan ^{-1}\left(\frac{\sqrt{3}}{\sqrt{2}}\right)$
(d) $\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$

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Key Concepts

Magnetic Dip (Inclination)

This concept refers to the angle that the Earth’s magnetic field makes with the horizontal plane. It indicates the extent to which the magnetic field lines are inclined, reflecting the vertical component of the magnetic force in contrast to the horizontal component, which is crucial in geomagnetism.

Magnetic Meridian

The magnetic meridian is the vertical plane that contains the Earth’s magnetic field and runs in the north-south direction. It serves as a reference frame for determining the directional behavior of magnets and other magnetic bodies in a geographic context.

Suspended Magnet Equilibrium

This concept involves the behavior of a magnet that is free to rotate about a vertical axis. The magnet aligns itself according to the resultant components of the Earth’s magnetic field, and its equilibrium orientation can reveal information about both the horizontal and vertical components of the field.

Vector Decomposition of Magnetic Field

This key concept involves breaking down the Earth’s magnetic field into its horizontal and vertical components. Understanding this decomposition is essential for analyzing phenomena like the dip angle, where the inclination of the field provides insights into the spatial distribution of magnetic forces.

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