Name the elements of the earth's magnetic field.
(N/A) The earth's magnetic field at any point on the surface is completely specified by three physical quantities, which are known as the elements of the earth's magnetic field:
$1$. Magnetic Declination $(\theta)$: The angle between the geographic meridian and the magnetic meridian at a place.
$2$. Magnetic Inclination or Angle of Dip $(\delta)$: The angle made by the total magnetic field vector of the earth with the horizontal direction in the magnetic meridian.
$3$. Horizontal Component of the Earth's Magnetic Field $(B_H)$: The component of the earth's total magnetic field vector along the horizontal direction in the magnetic meridian.
$1$. Magnetic Declination $(\theta)$: The angle between the geographic meridian and the magnetic meridian at a place.
$2$. Magnetic Inclination or Angle of Dip $(\delta)$: The angle made by the total magnetic field vector of the earth with the horizontal direction in the magnetic meridian.
$3$. Horizontal Component of the Earth's Magnetic Field $(B_H)$: The component of the earth's total magnetic field vector along the horizontal direction in the magnetic meridian.
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Assertion : The true geographic north direction is found by using a compass needle.
Reason : The magnetic meridian of the earth is along the axis of rotation of the earth.
Reason : The magnetic meridian of the earth is along the axis of rotation of the earth.
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 the dip angle is $\pm 45^{\circ}$.
$B_v = \text{vertical component of magnetic field} = \frac{\mu_0}{4\pi} \frac{2m \cos \theta}{r^3}$
$B_H = \text{horizontal component of magnetic field} = \frac{\mu_0}{4\pi} \frac{m \sin \theta}{r^3}$
where $\theta = 90^{\circ} - \text{latitude}$ as measured from the magnetic equator.
$(a)$ Find the loci of points for which the dip angle is $\pm 45^{\circ}$.
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