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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$A$ short bar magnet placed in a horizontal plane has its axis aligned along the north-south direction. Null points are found on the axis of the magnet at $20 \ cm$ from the centre of the magnet. The Earth's magnetic field at the place is $B$ and the angle of dip is $0^{\circ}$. If the total magnetic field on the normal bisector of the magnet at $20 \ cm$ from the centre of the magnet is $0.6 \ G$,then the magnitude of $B$ is: (in $G$)

Answer the following questions:
$(a)$ The earth's magnetic field varies from point to point in space. Does it also change with time? If so,on what time scale does it change appreciably?
$(b)$ The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?
$(c)$ The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the 'battery' (i.e.,the source of energy) to sustain these currents?
$(d)$ The earth may have even reversed the direction of its field several times during its history of $4$ to $5$ billion years. How can geologists know about the earth's field in such distant past?
$(e)$ The earth's field departs from its dipole shape substantially at large distances (greater than about $30,000\; km$). What agencies may be responsible for this distortion?
$(f)$ Interstellar space has an extremely weak magnetic field of the order of $10^{-12}\; T$. Can such a weak field be of any significant consequence? Explain.

The lines of force due to the Earth's horizontal component of the magnetic field are:

The earth's magnetic field at the equator is approximately $0.4 \; G$. Estimate the earth's dipole moment.

The dip angle in a vertical plane at an angle of $\cos^{-1} \left( \frac{1}{\sqrt{2}} \right)$ from the magnetic meridian is $60^\circ$. Find the actual dip angle at that place.

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