Question

The vertical component of the earth's magnetic field is:
(A) Zero at the magnetic pole
(B) Zero at the geographic pole
(C) Same Everywhere
(D) Zero at the magnetic equator

Answer 1

Hint Using the vertical component of magnetic field formula , $B.V = B \times \sin \theta$, identify for which angle of $\theta$ will the vertical component of earth’s magnetic field will become zero. Justify your answer using the same equation.

Complete Step By Step Solution
Earth’s magnetic field is a vector quantity where a it has strength and direction at each and every point in space. The magnetic field is split into 3 different components namely, field intensity of magnetic vector, horizontal intensity and vertical component of magnetic field.
Magnetic field lines aren’t straight lines and are rather curved in nature, which makes it changing in direction and magnitude at every point. In order to understand its nature at poles and any part of earth’s surface, we use a Cartesian system to split magnetic vectors into horizontal components, which are along the plane tangent to the equator line and vertical component, which is along the plane parallel to the equator.
Now, magnetic field intensity at any point at the vertical component is given as $B.V = B \times \sin \theta$. Now , at poles, the angle will be greater which results in higher magnetic field intensity. Thus greater the $\theta$value , greater the magnitude.
At equator, the $\theta$ value comes down nearly to zero , which results in zero magnitude at the equator point, since $\sin 0 = 0$.

Thus , Option(d) Is the correct option for the given question.

Note Magnetic field is defined as the space of area or field that describes magnetic influence on neighboring charges, material or moving particles in which a magnetic force is observed. Magnetic field intensity is determined by magnetic force and number of field lines passing.