Q.The vertical component of the Earth's magnetic field at a place is equal to the horizontal component. What is the value of the angle of dip at this place?

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:

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. …