Q.What happens to compass needles at the Earth's poles?

$\tan(\text{dip}) = B_V/B_H$; equal components give dip = 45°.

The angle of dip $\delta$ at a place is related to the horizontal ($B_H$) and vertical ($B_V$) components of the Earth's magnetic field by:

$\tan\delta = \dfrac{B_V}{B_H}$

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The angle of dip is found from tan(dip) = vertical component / horizontal component of Earth's field.

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When the horizontal and vertical components of Earth's magnetic field are equal, the angle of dip is 45°.

The angle of dip $\delta$ at a place relates the vertical component $B_V$ and horizontal component $B_H$ of Earth's magnetic field by

$\tan\delta = \dfrac{B_V}{B_H}$ …

$B = B_H/\cos\delta = 0.26/\cos60° = 0.52$ G.

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Angle of dip is 90° at the magnetic poles, 0° at the magnetic equator.

The angle of dip (inclination) δ is the angle the earth's total magnetic field makes with the horizontal. At the magnetic poles the field is entirely vertical, so a freely suspended dip needl …

Horizontal component B_H = B cos δ; vertical component B_V = B sin δ.

The earth's total magnetic field B makes an angle δ (the dip) with the horizontal. Resolving it:

$B_H = B\cos\delta, \qquad B_V = B\sin\delta$

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The angle of dip is the angle the Earth's total magnetic field makes with the horizontal; at the poles the field is purely vertical.

The angle of dip $\delta$ satisfies $\tan\delta = \dfrac{B_V}{B_H}$, where $B_V$ and $B_H$ are the vertical and horizontal components of the Earth's magnetic field.

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The vertical component of Earth’s magnetic field is found using $B_V = B \sin \delta$, where $B = 0.3$ G and $\delta = 30^\circ$. The result is $0.15$ G.

Using $H = B\cos\delta$, the total field $B = H/\cos\delta = 0.16/\cos 60° = 0.32$ G.

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At the magnetic equator the field is entirely horizontal, so the vertical component $B_V=0$ and the angle of dip $\delta=0$.

The Earth's magnetic field at any point can be resolved into a horizontal component $B_H$ and a vertical component $B_V$, related to the total field $B$ and the angle of dip $\delta$ by

$B_H = B\cos\delta,\qquad B_V = B\sin\delta$

At the magnetic equator, the Earth's field lines run parallel to the surface (purely horizontal), so the angle of dip $\delta = 0^\circ$. Hence

$B_V = B\sin 0^\circ = 0$ …

Angle of dip at the magnetic poles = 90°.

The angle of dip is the angle the Earth's total magnetic field makes with the horizontal. At the magnetic poles the field is entirely vertical (horizontal component B_H = 0), so a dip needle points vertically an …

Angle of dip is the angle earth's magnetic field makes with the horizontal; at the magnetic poles it equals 90 degrees.

Definition: At any place the earth's magnetic field can be resolved into a horizontal component (H) and a vertical component (V). The angle of dip (delta) is the angle by which the total field B dips below the horizontal, i.e. tan(delta) = V/H.

At the magnetic equator the field is purely horizontal, so V = 0 and delta = 0 degrees. …