The earth is made up of four primary layers: the inner core, outer core, mantle, and crust.The outer core is more than 800 miles and less than 2,200 miles from the Earth's center. Which of the following inequalities represents all possible distances, d, in miles, from the Earth's center that are in the outer core?

Read the following text and answer the following questions on the basis of the same: If we move into space and study the Earth's invisible magnetic field, it wouldn't really look like a bar magnet at all. Earth's magnetic field gets stretched out into a comet-like shape with a tail of magnetism that stretches millions of miles behind the earth, opposite to the Sun. The Sun has a wind of gas that pushes the earths field from the left to the right in the picture. The core of the Earth is an electromagnet. Although the crust is solid, the core of the Earth is surrounded by a mixture of molten iron and nickle. The magnetic field of Earth is caused by currents of electricity that flow in the molten core. These currents are hundreds of miles wide and flow at thousands of miles per hour as the Earth rotates. The powerful magnetic field passes out through the core of the Earth, passes through the crust and enters space. This picture shows the solid inner core region (inner circle) surrounded by a molten outer core (the area between the two circles). The currents flow in the outer core, travel outwards through the rest of the earth's interior. If the Earth rotated faster, it would have a stronger magnetic field. By the time the field has reached the surface of Earth, it has weakened a lot, but it is still strong enough to keep your compass needles pointed towards one of its poles. All magnets have two poles: a North Pole and a South Pole. The magnetic poles of earth are not fixed on the surface, but wander quite a bit. The pole in the Northern Hemisphere seems to be moving northwards in geographic latitude by about 10 kilometres per year by an average. Earth's magnetic field has a:

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate 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 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. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]

Answer the following questions: (a) The earth's magnetic field varies from point to point in space. Does is 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 earth's magnetism, why? (c) The charged currents in the outer conducting regions of earth's core are thought to be possible for earth's magnetism. What might be the battery 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 geologist 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 30000km). 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.

A point object with a charge +Q is placed at the center of a conducting shell of inner radius R , outer radius 2R, and a charge of -4Q . A thin - walled conducting shell of radius 3 R and a charge of +4Q is concentric with the point object and the first shell. Defining V = 0 at infinity, find all the distances from the center at which the electric potential is zero .

Read the following text and answer the following questions on the basis of the same: Band theory of solid: Consider that the Si or Ge crystal contains N atoms. Electrons of each atom will have discrete energies in different orbits. The electron energy will be same if all the atoms are isolated, i.e., separated from each other by a large distance. However, in a crystal, the atoms are close to each other (2 Å to 3 Å) and therefore the electrons interact with each other and also with the neighbouring atomic cores. The overlap (or interaction) will be more felt by the electrons in the outermost orbit while the inner orbit or core electron energies may remain unaffected. Therefore, for understanding electron energies in Si or Ge crystal, we need to consider the changes in the energies of the electrons in the outermost orbit only. For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4). The number of electrons in the outermost orbit is 4 (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N. The maximum possible number of outer electrons in the orbit is 8 (2s + 6p electrons). So, out of the 4N electrons, 2N electrons are in the 2N s-states (orbital quantum number l = 0) and 2N electrons are in the available 6N p-states. Obviously, some p-electron states are empty. This is the case of well separated or isolated atoms. The maximum possible electrons in an orbit is: