Hysteresis Loop

Hysteresis:

When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again. This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

Hysteresis Loop

It is customary to plot the magnetization M of the sample as a function of the magnetic field strength H, since H is a measure of the externally applied field which drives the magnetization .

u = 0

v = 60 km/hr = 16.67 m/s

t = 2 min = 120s

using v = u + at

or a =( v - u) / t

we get a = 16.67 / 120 = 0.1389 m/s²

Ionization energies (IE) have to do with things called ions. Ions are atoms which have gained or lost electrons. The ionization energy is the amount of energy it takes to detach one electron from a neutral atom. Some elements actually have several ionization energies. When this is the case, we refer to them as the "first ionization energy" or 'I', "second ionization energy" or 'I₂', and so on. Notice that the energy variable follows I_i where i is the orbital from which the electron is lost. Ionization is endothermic meaning that the atom or molecule increases its internal energy (takes energy from an outside source). The equation for the first ionization energy is shown below:

Na --> Na⁺ + e^-

The equation for the second ionization energy is:

Na⁺ --> Na²⁺ + e^-

Ionization energy values are typically very high and follow trends throughout the periodic table. The IE increase from bottom to top and left to right in the periodic table.

Below is a diagram showing the directions atomic size increase over the periodic table. As you can see, the IE and atomic size increase in opposite directions. This should make sense because as the atom gets smaller, the valence electrons become closer to the nucleus. This means the attractive force holding the electron is stronger and it takes more energy to pull the electron off.

Another trend is found when looking at the first IE of each atom. Below you can see the pattern when the IE is graphed against the atomic number. When looking at this diagram, you should notice that the increasing trend for atoms going horizontally across the periodic table is not absolute. This means that when you are looking at two atoms, the one furthest right does not always have the higher IE. However, there is an overall trend that shows an increasing IE the further right you are in the periodic table. These inconsistencies are attributed to the actual type of orbital the electron is being removed from. For instance, a 2p orbital has a higher energy than a 2s.

The ionization energy of an atom is equal to the amount of energy given off when an electron is added to an atom. When an electron is added to an atom, we call the energy given off the electron affinity (EA). So, IE=EA. For most atoms, the initial electron affinity is exothermic meaning energy is given off. However, when you try to add a second, third, etc. electron you are working with an already negative ion. Thus, it takes a greater energy to add the extra electron and therefore the EAs after this first are normally endothermic. A good approximation of electron affinity is the energy of the LUMO (lowest unoccupied molecular orbital). Electron affinities follow the same trends as the ionization energy across the periodic table as seen below.

The first of two main methods which scientists use to calculate the ionization energy is the Subtraction Method. This method entails some experimentation. You must first find the energy value of the ion you are looking for. Then subtract the energy value of the neutral atom. This difference is the ionization energy for that ion. Your answers can easily be checked against literature values published in most chemistry books. One such abbreviated table is shown below.

Ionization Energies in kJ/mol

	1	2	3	4	5	6	7	8
H	1312
He	2372	5250
Li	520	7297	11810
Be	899	1757	14845	21000
B	800	2426	3659	25020	32820
C	1086	2352	4619	6221	37820	47260
N	1402	2855	4576	7473	9442	53250	64340
O	1314	3388	5296	7467	10987	13320	71320	84070
F	1680	3375	6045	8408	11020	15160	17860	92010
Ne	2080	3963	6130	9361	12180	15240
Na	496	4563	6913	9541	13350	16600	20113	25666
Mg	737	1450	7731	10545	13627	17995	21700	25662

Tailing of mercury is the reaction of mercury with ozone due to which mercury looses its meniscus and it starts sticking to the waals of thermometer due to the formation of mercurous oxide. The meniscus can be restored by shaking it with water.

The reaction can be shown as :

If you are satisfie do give thumbs up.

Structure and Bonding of Dry Ice

A mole (abbreviated mol) of a pure substance is a mass of the material in grams that is numerically equal to the molecular mass in atomic mass units (amu). A mole of any material will contain Avogadro's number of molecules. For example, carbon has an atomic mass of exactly 12.0 atomic mass units -- a mole of carbon is therefore 12 grams. For an isotope of a pure element, the mass number A is approximately equal to the mass in amu. The accurate masses of pure elements with their normal isotopic concentrations can be obtained from the periodic table.

One mole of an ideal gas will occupy a volume of 22.4 liters at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure).

Avogadro's number, N_A = 6.0221367 X 10²³ / mol

The CM of rod (say mass M1) lying along x-axis is (L/ 2, 0)

Similarly, the CM of the rod (say mass M2) lying along y-axis is (0, L/ 2)

Now when the combination of two rods are considered in the given fashion then it is like finding the center of mass of the two objects of mass M1 and M2 kept at (L/ 2, 0) and (0, L/ 2) respectively

Thus it will lie on the line joining the two points that is (L/ 2, 0) and (0, L/ 2),

Now if coordinates of cente of mass are (X_cm, Y_cm)

Then X_cm< L/2 and Y_cm< L/2

therefore options (1) and (2) are ruled out.

Now since the two rods are made up of different materials thefore X_cm # Y_cmthis rules out option (3)

Therfore correct option is (4) (L/3, L/6)

Isomerism, the existence of molecules that have the same numbers of the same kinds of atoms (and hence the same formula) but differ in chemical and physical properties. The roots of the word isomer are Greek—isos plus meros, or “equal parts.” Stated colloquially, isomers are chemical compounds that have the same parts but are nonetheless not the same. To make a crude analogy, two bracelets, each consisting of five red and five green beads, could be arranged in many different isomeric forms, depending on the order of the colours. Each bracelet would have the same parts—that is, the five red and five green beads—but each variation would be different. One could also imagine combinations of those same beads in which pendant chains were attached to a bracelet in a variety of ways. One might imagine two bracelets of the same red-green order but with identical chains attached in different orientations. Such structures also would be analogous to isomers. In a more subtle analogy, one’s hands can be seen as isomeric. Each hand possesses the same kinds of fingers, but a right hand can never be superimposed perfectly on a left hand; they are different. Timing and energy are also factors in isomerism. Molecules are mobile entities, undergoing all sorts of rotational motions that change their shapes, and those motions require energy. Thus, some molecules can be the same on one timescale or set of energy conditions but different, or isomeric, on others. Finally, an isomer must be an energy minimum; it must lie in an energy well. There are two general types of isomers. Constitutional isomers are molecules of different connectivity—analogous to simple bracelets in which the order of red and green beads is different. The second type is stereoisomers. In stereoisomers the connectivity is the same, but the parts are oriented differently in space.

Using Kepler's third law of Planetary motion i.e.

The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

or T² = k R³ (where k is proportionality constant)

Therefore when the separation between the earth and the satellite is increased to 4 times we have new time period T₂ given by

(T₁ / T₂)²= ( R₁ /R₂)³

or 5/T₂ = (1/4)^3/2

or T₂ = 5*8 = 40 hours

Electricity is the set of physical phenomena associated with the presence and flow of electric charge. Electricity gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and the flow of electrical current. In addition, electricity permits the creation and reception of electromagnetic radiation such as radio waves.

In electricity, charges produce electromagnetic fields which act on other charges.

Electricity occurs due to several types of physics:

a) electric charge: a property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields.

b) electric current: a movement or flow of electrically charged particles, typically measured in amperes.

c) electric field: an especially simple type of electromagnetic field produced by an electric charge even when it is not moving (i.e., there is no electric current). The electric field produces a force on other charges in its vicinity. Moving charges additionally produce a magnetic field.

d) electric potential: the capacity of an electric field to do work on an electric charge, typically measured in volts.

e) electromagnets: electrical currents generate magnetic fields, and changing magnetic fields generate electrical currents

In electrical engineering, electricity is used for:

a) electric power where electric current is used to energise equipment

b) electronics which deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies.

Electrical phenomena have been studied since antiquity, though advances in the science were not made until the seventeenth and eighteenth centuries. Practical applications for electricity however remained few, and it would not be until the late nineteenth century that engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society. Electricity's extraordinary versatility as a means of providing energy means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. Electrical power is the backbone of modern industrial society.[1]

2A is simply the matrix A with all its entries multiplied by 2.

Using the identity: det(AB) = det(A)det(B) where A and B are matrices.

In our case det (AB) = det (2A)

where, B=2I and I is the identity matrix and detB is therefore 8.

So det2A=8 detA

or det (-2A) = -8 det (A)

The Na2 contributes +2 to oxidation number, so S4O6 is -2. O6 contributes -12, so S4 is +10, and each S is +10/4 = +5/2.

When a ray of light enters the glass slab from air, its frequency and does not change at all. However, its speed will decrease, and it will bend also. This is called as refraction phenomenon. Its wavelength will also change , and it can be calculated by the following formula,

refractive index x lambda = lambda₀

where,

Lambda₀ is the wavelength in a vacuum

lambda is the wavelength in the medium

A semiconductor is a material which has electrical conductivity between that of a conductor such as copper and an insulator such as glass. The conductivity of a semiconductor increases with increasing temperature, behaviour opposite to that of a metal. Semiconductors can display a range of useful properties such as passing current more easily in one direction than the other. Because the conductive properties of a semiconductor can be modified by controlled addition of impurities or by the application of electrical fields or light, semiconductors are very useful devices for amplification of signals, switching, and energy conversion. Understanding the properties of semiconductors relies on quantum physics to explain the motions of electrons through a lattice of atoms.

Current conduction in a semiconductor occurs via free electrons and "holes", collectively known as charge carriers. Adding impurity atoms to a semiconducting material, known as "doping", greatly increases the number of charge carriers within it. When a doped semiconductor contains excess holes it is called "p-type", and when it contains excess free electrons it is known as "n-type". The semiconductor material used in devices is doped under highly controlled conditions to precisely control the location and concentration of p- and n-type dopants. A single semiconductor crystal can have multiple p- and n-type regions; the p–n junctions between these regions have many useful electronic properties.

Semiconductors are the foundation of modern electronics, including radio, computers, and telephones. Semiconductor-based electronic components include transistors, solar cells, many kinds of diodes including the light-emitting diode (LED), the silicon controlled rectifier, photo-diodes, and digital and analog integrated circuits. Increasing understanding of semiconductor materials and fabrication processes has made possible continuing increases in the complexity and speed of semiconductor devices, an effect known as Moore's law.

Rotation of Plane-Mirror

Figure. The angle of reflection
is twice the angle of rotation of
the mirror.

Consider a plane-mirror and a fixed incident ray of light reflecting from the surface at an angle θ_i. Before the mirror has rotated, the angle of incidence is θ as is the angle of reflection. If the mirror is rotated through an angle φ the normal is rotated by an angle &phi and thus the angle of incidence increases to θ +φ. Therefore, the angle of reflection must also increase by φ to θ+φ The difference between the final angle of reflection and the initial angle of reflection and is 2φ

NOTE: For a fixed incident ray, the angle of the reflection is twice the angle through which the mirror has rotated. &thetaf= 2φ

Following theory is vital for the solution provided for above numerical

Height of Transmitting Antenna

If the broadcast is made from a height h above the ground, no reception by direct signals is possible beyond the points A and B.

The distance up to which signals can be received can be calculated in terms of h and the radius R of the Earth.

In the right-angled triangle CBP,

CP²= CB² + BP²

But, CP = R + h

R²+ h² + 2Rh = R²+ d²

d² = h²+ 2Rh

h = 100 m, R= 6.37 x 10⁶m,

Therefore total area = 2 π * 100 * (6.37 * 10⁶) = 1.28 π X 10⁹

Unit vector along z-axis is simlpy k i.r. 0i + 0j + k

However if you wish to find component of vecor 2i+3j-5k along z-axis then it is -5

Also unit vecor parallel to 2i+3j-5k is 2i+3j-5k / (4 + 9 + 25 )^0.5= 2i+3j-5k / Root(38)

All charges will reside only on the surface of the solid spherical conductor

The basic thing to understand here is that electrons flow freely within conductors. The electric potential at all points in a conducting body should be equal. Otherwise since in a conductor charges are free flowing, the charges would freely flow and redistribute themselves until potential is equalized. Since there is no potential difference between any two points within the conducting body, there cannot be any electric field inside the solid conducting sphere. Since there is not electric filed inside the solid sphere, there cannot be any charge distribution inside the sphere (from Gauss law if there where any charge distribution inside the sphere, there would be an electric field). This leads to an inescapable conclusion that charges in the conducting sphere will only reside on the surface of the sphere. In other there will only be a surface charge density in the solid sphere.

Hysteresis Loop

Ionization Energies in kJ/mol

Structure and Bonding of Dry Ice

Rotation of Plane-Mirror

Height of Transmitting Antenna

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