CBSE Class 12 Physics Chapter 5: Magnetism and Matter NCERT Solutions

(a) The Earth's magnetic field at any point on the surface can be completely specified using three independent quantities:

1. Magnetic declination: This is the angle between the geographic meridian and the magnetic meridian at that location.
2. Angle of dip (or inclination): This is the angle that the Earth's magnetic field lines make with the horizontal plane at that location.
3. Horizontal component of the Earth's magnetic field (B_H): This is the component of the Earth's magnetic field that lies in the horizontal plane.

(b) The angle of dip is generally larger at higher latitudes (closer to the magnetic poles) and smaller at lower latitudes (closer to the magnetic equator). Britain is at a higher latitude than southern India and is closer to the Earth's magnetic North Pole. Therefore, you would expect a greater dip angle in Britain compared to southern India.

(c) The Earth's magnetic field lines emerge from the magnetic North Pole and enter the magnetic South Pole. Conventionally, the Earth's magnetic South Pole is located near the geographic North Pole, and the magnetic North Pole is near the geographic South Pole. Melbourne, Australia, is in the Southern Hemisphere, closer to the Earth's magnetic North Pole. Therefore, the magnetic field lines would generally be directed outwards from the Earth's surface in this region. So, the lines would seem to come out of the ground at Melbourne.

(d) If a compass is located exactly on the geomagnetic North Pole or South Pole, the Earth's magnetic field lines are oriented vertically. A compass needle, which is free to move in the vertical plane, would align itself with the vertical magnetic field. At the geomagnetic North Pole, it would point vertically downwards into the Earth, and at the geomagnetic South Pole, it would point vertically upwards out of the Earth.

(e) To check the order of magnitude of the Earth's magnetic field due to a dipole of magnetic moment $M\; =\; 8\; \backslash times\; 10^\{22\}\; \backslash text\{\; J\; T\}^\{-1\}$ at its center, we can calculate the field strength at the Earth's surface. The radius of the Earth is approximately $r\; =\; 6.4\; \backslash times\; 10^6\; \backslash text\{\; m\}$. The magnetic field strength (B) at a distance r from the center of a dipole is given by $B\; =\; \backslash frac\{\backslash mu\_0\; M\}\{4\backslash pi\; r^3\}$ (considering a point on the equator for simplicity, or average field). Using $\backslash mu\_0\; =\; 4\backslash pi\; \backslash times\; 10^\{-7\}\; \backslash text\{\; T\; m\; A\}^\{-1\}$:

$$B\; =\; \backslash frac\{(4\backslash pi\; \backslash times\; 10^\{-7\}\; \backslash text\{\; T\; m\; A\}^\{-1\})\; \backslash times\; (8\; \backslash times\; 10^\{22\}\; \backslash text\{\; J\; T\}^\{-1\})\}\{4\backslash pi\; \backslash times\; (6.4\; \backslash times\; 10^6\; \backslash text\{\; m\})^3\}$$

$$B\; =\; \backslash frac\{10^\{-7\}\; \backslash times\; 8\; \backslash times\; 10^\{22\}\}\{(6.4)^3\; \backslash times\; 10^\{18\}\}\; \backslash text\{\; T\}$$

$$B\; =\; \backslash frac\{8\; \backslash times\; 10^\{15\}\}\{262.144\; \backslash times\; 10^\{18\}\}\; \backslash text\{\; T\}\; \backslash approx\; 3.05\; \backslash times\; 10^\{-5\}\; \backslash text\{\; T\}$$

This value is approximately 0.3 Gauss (since $1\; \backslash text\{\; T\}\; =\; 10^4\; \backslash text\{\; G\}$). This is of the order of magnitude of the Earth's magnetic field observed at the surface (typically 0.25 to 0.65 Gauss), confirming the dipole approximation's validity in terms of magnitude.

(f) Geologists can find local magnetic poles due to the presence of magnetised mineral deposits within the Earth's crust. These deposits, such as certain iron ores, can possess their own strong magnetic fields that are localised and oriented in various directions, independent of the main dipole field of the Earth. These local variations create anomalies in the Earth's overall magnetic field pattern.

(a) Yes, the Earth's magnetic field does change with time. These changes occur on various time scales. Short-term variations (over days, months, or years) are relatively small but measurable. However, significant changes, including reversals of the magnetic field, occur over much longer geological time scales, typically thousands to millions of years. Secular variation refers to the slow drift in the magnetic field's direction and intensity over decades.

(b) While the Earth's core contains iron, which is a ferromagnetic material, it is not the direct source of the Earth's magnetism. The core is extremely hot, far above the Curie temperature for iron. At these temperatures, iron loses its ferromagnetic properties and behaves paramagnetically. The Earth's magnetism is believed to be generated by a dynamo effect, involving the motion of molten, electrically conductive material (like iron and nickel) in the Earth's outer core.

(c) The 'battery' or the source of energy to sustain the electrical currents in the Earth's outer core is thought to be the thermal energy generated by radioactive decay within the Earth and the residual heat from the planet's formation. This thermal energy drives convection currents in the molten outer core. The motion of this conductive fluid, combined with the Earth's rotation (Coriolis effect), generates electrical currents and, consequently, the Earth's magnetic field through a self-sustaining dynamo process.

(d) Geologists can determine the Earth's magnetic field direction from the distant past through the study of paleomagnetism. When certain igneous rocks, like basalt, cool from a molten state (lava), magnetic minerals within them (such as magnetite) align themselves with the prevailing direction of the Earth's magnetic field at that time. This alignment is locked in as the rock solidifies. By studying the magnetic orientation of these minerals in ancient rock formations of different ages, geologists can reconstruct the history of the Earth's magnetic field, including its reversals.