The magnetic field and angle of dip at a place on the earth are $0{\cdot}3$ G and $30^\circ$, respectively. The value of vertical component of the earth's magnetic field at the place is ___________ .

The magnetic field and angle of dip at a place on the earth are 0·3 G and 30^°, respectively. The value of ver

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0{\cdot}3

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Concept understanding — Angle of Dip

What Is the Angle of Dip? A First Look

Imagine standing in an open field with a compass. The needle points roughly north — that much you know. But if you could watch that needle in three dimensions, you'd notice something else: in most places on Earth, the needle doesn't lie perfectly flat. One end tilts downward, as if it's trying to point into the ground. That tilt is the angle of dip (also called the magnetic inclination).

The Earth's magnetic field is not horizontal. It enters and exits the ground at an angle, depending on where you are. At the magnetic equator, the field runs parallel to the surface — no tilt. At the magnetic poles, it points straight down. Everywhere else, it's somewhere in between.

The Precise Definition

The angle of dip ( $\delta$ ) is the angle that the Earth's total magnetic field vector $\vec{B}_\text{total}$ makes with the horizontal plane.

If you break the total field into two perpendicular components:

$B_H$ — the horizontal component (parallel to the ground)
$B_V$ — the vertical component (pointing into or out of the ground)

then the angle of dip is given by:

\tan \delta = \frac{B_V}{B_H}

\delta = \tan^{-1}\left( \frac{B_V}{B_H} \right)

What the Sign Tells You

Positive dip ( $B_V$ downward): the north-seeking end of the needle dips below the horizontal. This happens in the northern hemisphere.
Negative dip ( $B_V$ upward): the north-seeking end rises above the horizontal. This happens in the southern hemisphere.
Zero dip ( $B_V = 0$ ): the field is entirely horizontal. This occurs along the magnetic equator.

At the magnetic poles, $B_H = 0$ and $B_V$ is maximum, so $\delta = 90^\circ$ — the needle points straight down (or up).

Why It Matters

The angle of dip is not a textbook curiosity. Navigators use it to correct compass readings near the poles. Geologists map it to understand the Earth's interior. And in your exams, it connects the components of the magnetic field in a clean trigonometric relation — one that lets you calculate any component if you know the total field strength and the dip angle. …

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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.

The Earth’s magnetic field at any location has both horizontal and vertical components. The angle of dip (or magnetic inclination) $\delta$ is the angle that the total field $\mathbf{B}$ makes with the horizontal plane. If you imagine the total field vector pointing into the ground at an angle, its vertical part is simply the projection along the downward direction.

The relationship is purely trigonometric:

Horizontal component: $B_H = B \cos \delta$
Vertical component: $B_V = B \sin \delta$

Here, we are given the total field $B = 0.3$ G (gauss) and the dip angle $\delta = 30^\circ$ . We need $B_V$ .

Write the formula for the vertical component:

B_V = B \sin \delta

Substitute the given values:

B_V = 0.3 \times \sin 30^\circ

Recall that $\sin 30^\circ = \frac{1}{2} = 0.5$ .

B_V = 0.3 \times 0.5 = 0.15

The unit remains gauss (G), since both $B$ and $B_V$ are in the same unit. …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL1 mark
$Q. If the horizontal and vertical components of earth's magnetic field are equal at a place, find the angle of dip.$
›Reveal solutionSolution

$\tan(\text{dip}) = B_V/B_H$ ; 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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CBSE 2023Set ANNUAL1 markMCQ
$Q. The vertical component of earth's magnetic field at a place is sqrt(3) times the horizontal component. The value of angle of dip at this place is$
(1) 30 degrees
(2) 45 degrees
(3) 60 degrees
(4) 90 degrees
›Reveal solutionSolution

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

…

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CBSE 2023Set ANNUAL1 markMCQ
$Q. At a given place the horizontal and vertical components of earth's magnetic field are equal. The angle of dip at that place will be:$
(a) 0°
(b) 45°
(c) 60°
(d) 90°
›Reveal solutionSolution

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

$\tan\delta = \dfrac{B_V}{B_H}$ …

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CBSE 2023Set ANNUAL1 markMCQ
$60°$
(a) 0.50G
(b) 0.52G
(c) 0.54G
(d) 0.56G
›Reveal solutionSolution

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

…

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CBSE 2021Set A1 markMCQ
$Q. The value of angle of dip at magnetic pole of the earth is (A) 0° (B) 90° (C) 45° (D) 180°$
›Reveal solutionSolution

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 …

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CBSE 2021Set A1 markMCQ
$Q. If B is earth's magnetic field in magnetic meridian, δ is angle of dip, B_H is horizontal component of B and B_V is vertical component of B, then which of the following relations is correct? (A) B_H = B cosδ (B) B_V = B cosδ (C) B_H = B sinδ (D) B_V = B_H sinδ$
›Reveal solutionSolution

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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CBSE 2021Set OC1 markMCQ
$Q. At the poles, the angle of dip is$
(a) $45^\circ$
(b) $30^\circ$
(c) $0^\circ$
(d) $90^\circ$
›Reveal solutionSolution

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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CBSE 2020Set 55/1/11 mark
$0{\cdot}3$
›Reveal solutionSolution
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.

The Earth’s magnetic field at any location has both horizontal and vertical components. The angle of dip (or magnetic inclination) $\delta$ is the angle that the total field $\mathbf{B}$ makes with the horizontal plane. If you imagine the total field vector pointing into the ground at an angle, its vertical part is simply the projection along the downward direction.

The relationship is purely trigonometric:

Horizontal component: $B_H = B \cos \delta$

Vertical component: $B_V = B \sin \delta$

Here, we are given the total field $B = 0.3$ G (gauss) and the dip angle $\delta = 30^\circ$ . We need $B_V$ .

Write the formula for the vertical component:

$B_V = B \sin \delta$

Substitute the given values:

$B_V = 0.3 \times \sin 30^\circ$

Recall that $\sin 30^\circ = \frac{1}{2} = 0.5$ .

$B_V = 0.3 \times 0.5 = 0.15$

The unit remains gauss (G), since both $B$ and $B_V$ are in the same unit. …
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CBSE 2020Set ANNUAL1 markMCQ
$Q. In the magnetic meridian at a certain location, the horizontal component of earth's magnetic field is 0.16 G and angle of dip is 60°. The earth's magnetic field at this location is: (A) 0.32 G (B) 0.36 G (C) 0.18 G (D) 0.16 G$
›Reveal solutionSolution

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

…

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CBSE 2019Set ANNUAL1 mark
$Q. Where on the surface of the earth is the vertical component of earth's magnetic field zero?$
›Reveal solutionSolution

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

$B_V = B\sin 0^\circ = 0$ …

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CBSE 2019Set ANNUAL1 markMCQ
$Q. The value of angle of dip at the earth's magnetic pole is -$
(a) 0°
(b) 45°
(c) 90°
(d) 180°
›Reveal solutionSolution

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 …

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CBSE 2019Set ANNUAL1 mark
$Q. Define angle of dip. Write value of angle of dip at magnetic poles of earth.$
›Reveal solutionSolution

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. …

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Q.The magnetic field and angle of dip at a place on the earth are 0⋅30{\cdot}30⋅3 G and 30∘30^\circ30∘, respectively. The value of vertical component of the earth's magnetic field at the place is ___________ .

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Q.The magnetic field and angle of dip at a place on the earth are $0{\cdot}3$ G and $30^\circ$ , respectively. The value of vertical component of the earth's magnetic field at the place is ___________ .

Unlock everything free for 14 days