What are the Earth's magnetic elements? Define them and list them.

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(N/A) To completely describe the Earth's magnetic field at any point on its surface,three physical quantities are required,which are known as the magnetic elements of the Earth. These are:
$(1)$ Magnetic Declination $(D)$: The angle between the geographic meridian and the magnetic meridian at a place.
$(2)$ Magnetic Inclination or Dip Angle $(I)$: The angle that the total magnetic field vector of the Earth makes with the surface of the Earth (horizontal) in the magnetic meridian.
$(3)$ Horizontal Component of Earth's Magnetic Field $(H_E)$: The component of the Earth's total magnetic field vector in the horizontal direction in the magnetic meridian. It is related to the total field $B_E$ and dip angle $I$ by $H_E = B_E \cos(I)$.

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What is the most accepted scientific explanation for the origin of the Earth's magnetic field?

At a certain place,the angle of dip is $30^{\circ}$ and the horizontal component of the Earth's magnetic field is $0.50 \text{ Oersted}$. The Earth's total magnetic field is:

The relation between $Z_E, H_E$,and $B_E$ is . . . . . . .

The vertical component of the earth's magnetic field is zero at a place where the angle of dip is.....$^o$

Assume the dipole model for Earth's magnetic field $B$,which is given by:
$B_{V} = \text{vertical component of magnetic field} = \frac{\mu_{0}}{4\pi} \frac{2m \cos \theta}{r^{3}}$
$B_{H} = \text{horizontal component of magnetic field} = \frac{\mu_{0}}{4\pi} \frac{m \sin \theta}{r^{3}}$
where $\theta = 90^{\circ} - \text{latitude}$ as measured from the magnetic equator.
$(a)$ Find the loci of points for which $|\vec{B}|$ is minimum.

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