CBSE Class 12 Physics Chapter 10: Magnetism and Matter NCERT Solutions

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

1. Magnetic declination: The angle between the geographic meridian and the magnetic meridian at that location.
2. Angle of dip (or magnetic inclination): The angle that the Earth's magnetic field lines make with the horizontal plane at that location.
3. Horizontal component of Earth's magnetic field: The strength of the magnetic field along the horizontal direction.

(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. The dip angle in Britain is approximately 70°, which is significantly greater than 18°.

(c) The Earth's magnetic field lines emerge from the magnetic North Pole and enter the magnetic South Pole. Conventionally, the 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 magnetic North Pole. Therefore, magnetic field lines would generally be expected to enter the ground (pointing towards the magnetic North Pole) in this region.

(d) If a compass is located exactly on the geomagnetic North Pole or South Pole, the Earth's magnetic field lines are vertical. A compass needle, which is free to move in the vertical plane, would align itself vertically. However, if it's free to move in the horizontal plane, it can point in any direction because there is no preferred horizontal direction at the poles.

(e) To check the order of magnitude of the Earth's magnetic dipole moment (M = 8 \times 10^{22} \text{ J T}^{-1}), we can compare it with the magnetic field strength at the Earth's surface. The magnetic field (B) due to a dipole at a distance (r) is approximately B = \frac{\mu_0 M}{4\pi r^3}. Using the Earth's radius r \approx 6.4 \times 10^6 m and the permeability of free space \mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}, we get:

B = \frac{(4\pi \times 10^{-7} \text{ T m A}^{-1}) \times (8 \times 10^{22} \text{ J T}^{-1})}{4\pi \times (6.4 \times 10^6 \text{ m})^3} \approx \frac{8 \times 10^{15}}{2.62 \times 10^{20}} \text{ T} \approx 3.8 \times 10^{-5} \text{ T}

This value is approximately 38 microteslas (\mu T), which is of the order of magnitude of the Earth's actual magnetic field (around 25 to 65 \mu T), confirming the claim.

(f) Local magnetic poles can exist due to the presence of magnetized mineral deposits within the Earth's crust. These deposits, such as iron ore formations, can possess their own magnetic fields that are strong enough to create local variations or poles, superimposed on the Earth's main dipole field. These local fields can be oriented in various directions depending on the geological structure.

(a) Yes, the Earth's magnetic field does change with time. These changes occur on various time scales. Short-term variations (seconds to years) include fluctuations due to solar activity. Secular variations (decades to millennia) involve slow changes in the field's intensity and direction, causing the magnetic poles to drift. Over geological time scales (hundreds of thousands to millions of years), the Earth's magnetic field has undergone complete reversals of its polarity.

(b) While the Earth's core contains iron, which is a ferromagnetic material, the high temperatures within the core exceed the Curie temperature for iron. Above the Curie temperature, materials lose their permanent ferromagnetic properties and behave paramagnetically. Therefore, the solid iron in the inner core is not the direct source of the Earth's magnetism. Instead, the magnetism is generated by the movement of molten, electrically conducting material (primarily iron and nickel) in the outer core, a process known as the geodynamo.

(c) The 'battery' or source of energy to sustain the electrical currents in the Earth's outer core is believed to be the thermal convection and the Coriolis forces acting on the molten, conducting fluid. Heat generated from radioactive decay within the Earth and residual heat from its formation drives convection currents. The Earth's rotation, through the Coriolis effect, organizes these convective motions into complex patterns, leading to the generation and maintenance of the geomagnetic field through the dynamo effect.

(d) Geologists can determine the Earth's magnetic field in the distant past by studying the magnetic properties of rocks. When molten lava cools and solidifies, magnetic minerals within it align themselves with the prevailing direction of the Earth's magnetic field at that time, becoming permanently magnetized. This preserved magnetization, known as paleomagnetism, acts like a fossil record of the Earth's field. By analyzing the direction of magnetization in rock layers of different ages, geologists can reconstruct the history of the Earth's magnetic field, including its reversals.