All the derivation is precisely explained.
You need to equate Newton second law to Lorentz equation, assuming the magnetic field is normal to current flow. You need do this separately for electrons and for holes. Both velocity and electric field have two components, transversal (y) and longitudinal (x) and the magnetic field is in z. It is more comfortable separate the vectorial equations into two equations, one for each component. So, you have four equations: 1) For time derivative of x-velocity of electrons 2) For time derivative of x-velocity of holes 3) For time derivative of y-velocity of electrons 4) For time derivative of y-velocity of holes
The set is complicate, but it is easier if you do the following approximation: If magnetic field is small, you can assume that the second term in equations 1) and 2) is negligible. Yo cannot do the same with equations 3) and 4) because, since mobility of electrons and holes are not much different, this would give you as a result that transversal field does not exist, and you will not get anything.
You must bear in mind that velocities in your equations are individual velocities and you need average velocities. If you use the single model of a carrier starting from zero velocity and accelerating at a constant rate and suddenly stopped at a time tau, you can obtain the average velocities for the four equations multiplying the right side of each times tau/2. You can make sense of all this by plotting changing velocity as a saw tooth signal.
In agreement with mobility definition (charge times half-tau over effective mass) you can see that equations 1) and 2) are no more that the classic lineal relation between average velocity and electric field, with the mobility as a constant. Equations 3) and 4) have both a similar first term but the second term, including the magnetic field is more weird.
Now, you have average x-velocity for electrons, average x-velocity for holes, average y-velocity for electrons and average y-velocity for holes. If you multiply each velocity by charge and concentration you will get x-current density for electrons, x-current density for holes, y-current density for electrons and y-current density for holes. When this is done, you can add contributions of both types of carriers and obtain x-current density and y-current density.
What you will use for calculating the Hall´s coefficient is transversal current density which must be zero. Replace this zero in the formula for y-current density and you will obtain two terms equated to zero or rearranging, an equality between two terms. One of the terms is already in the shape we want, but the other still include longitudinal velocities for electrons and holes. You have expressions for them and must replace in the expression for y-current density. Now, you must identify expressions that can be replaced by electron and hole mobilities.
Now, you only have carrier concentrations, carrier mobilities, longitudinal and transversal fields and magnetic field magnitude. Solve for transversal electric field. For obtaining Hall´s coefficient you need to multiply both numerator and denominator for conductivity. Keep conductivity in the denominator in terms of concentrations and mobilities. This is not important for the numerator because you will must note that conductivity times longitudinal electric field is longitudinal density current. Now you have transversal electric field as a linear function of the product of current density (longitudinal, the only non-zero current density) times the magnetic field magnitude. The proportionality constant is Hall´s coefficient.
Musician Daryl Hall, of the pop group Hall and Oates, was diagnosed with Lyme disease in 2005. He suffered on and off with the disease for three years, but is now cured.***I d…on't know if Lyme Disease can be "cured" but he's managing it.(MORE)
With the increase in temperature if the resistance increases or the current in the circuit decreases then it is said to be have positive temperature coefficient . But in semi-…conductors with the increase in temperature the electrons present in the valance band are excited and they would enter the conduction band for conduction . As the no. of charge carriers always increase in a semi-conductor , implies that the current always increases with the increase in temperature so the semi-conductor can never have positive temperature coefficient(MORE)
Soto-Hall test. This test is primarily employed when fracture of a vertebra is suspected. The patient is placed supine [lying on back] without pillows. One hand of the examine…r is placed on the sternum of the patient, and mild pressure is exerted to prevent flexion at either the lumbar or thoracic regions of the spine. The other hand of the examiner is placed under the patient's occiput [back of the head], and the head is slowly flexed toward the chest. Flexion of the head and neck on the chest progressively produces a pull on the posterior spinous ligaments from above, and when the spinous process of the injured vertebra is reached, an acute local pain is experienced by the patient.(MORE)
Having to find the derivative of a certain function is one of the basics upon which calculus in particular, and computational mathematics in general, is based. Unfortunately, …there is no one surefire way to find the derivative of all functions. Depending on the expressions within the function, the means for obtaining the derivative of this function varies from one function to the next. In many cases, you may have to apply several different rules simultaneously in order to find the derivative of a function. This article lists some of the formulas associated with finding the derivatives of various functions.Usually, when you are first introduced to finding the derivative, the first kind of derivative that you are asked to find is the derivative of a polynomial. This polynomial usually consists of several expressions that contain a certain variable that is raised to varying powers. In order to find the derivative of a polynomial, you need to subtract the power of the variable by one, and multiply the coefficient of the polynomial term by the original power.The exponential function e the power of x is one of the most singular expressions in mathematics. The unique thing about this particular expression is that its derivative is itself. This means that whenever you obtain the derivative of e-power-x, the derivative itself will be e-power-x. It is this particular property that makes the value e, Euler's constant, a universal constant in mathematics, as well as a transcendental number.Trigonometric functions are a special class of functions in mathematics. This is because they are periodical and interrelated. This can be illustrated by the fact that the derivative of the sine function is another trigonometric function: the cosine function. It is important to note that there are no sign changes when finding the derivative of the sine function. The derivative of the function is a cosine function with the exact same sign and the exact same expression.The derivative of the cosine function is another trigonometric derivative. Unlike the derivative of the sine function, the sign is not preserved when you obtain the derivative of cosine. The derivative of cosine is negative sine. This means that when you evaluate the derivative of a cosine function, you need to flip the sign of the resulting sine function. If the sign was originally positive, it becomes negative. Likewise, if the sign was originally negative, it becomes positive.Ln(X) is one final function of interest for which you might want to find the derivative. The derivative of this function is none other than 1/X. Evaluating the value which results in 1/X using conventional means is not possible, since the number must give negative 1 when the power of the variable has 1 subtracted from it. When you multiply the original value by the coefficient, the expression evaluates to be 0, which does not compute in the traditional sense.There are almost as many different kinds of derivatives as there are functions. Some of these are very commonly used, such as the derivatives of trigonometric functions and the derivatives of exponential functions. On the other hand, there are other derivatives that are much less likely to be used, such as the derivatives of Ln(X). The most important derivatives by far that you must know if you are to derive functions correctly in mathematics are the derivatives of polynomials. These are the most commonly recurring ones, both on exams and in real-life applications.If you have time to confirm your answer, you can integrate the function for which you found the derivative. If you find that the resulting integration is the original function, then you have carried out the derivation correctly.(MORE)
Pottery might seem like a rustic art, but there is a great deal of science behind it. Potters work with principles of physics and chemistry every time they practice their craf…t. The Coefficient of Expansion is a crucial concept to understand in order to achieve successful firing and glazing. Read more to find out what the coefficient of expansion is, how it applies to pottery, and what you need to know about it to achieve better results.The coefficient of expansion measures the degree of a material's expansion when it is heated and contraction when it is cooled. If something has a low coefficient of expansion, its size changes less when it is exposed to changes in temperature. If the coefficient is high, it changes more significantly. By changing the chemical makeup of a substance, the coefficient can be raised or lowered.Most ceramic objects expand as they are heated and contract as they are cooled. Often the body and glaze have different characteristics, but since the glaze is joined to it, it must conform to the changes in the body. It is important in pottery, then, for clay objects and their glazes to have similar coefficients of expansion. Otherwise, glaze defects will occur in the firing process.Crazing (cracks) and shivering (flaking) are two common results of mismatched coefficients of expansion between a pot and its glaze, when the two don't "fit together." These problems are not just aesthetic, either. Strength of the finished product can be compromised and so can its ability to be sanitized enough to function as dinnerware. The tension created by mismatched thermal expansion can also be enough to pull a piece apart unless a piece is glazed both inside and out.Crazing happens when a glaze has a higher expansion coefficient than the body. In other words, it not only expands more than the body when heated, it contracts more when it cools. This forces the glaze into a "too tight" fit over the body. This leads to a network of cracks. Crazing can be prevented by adjusting the "recipe" of the clay body so they both shrink at a comparable rate. Crazing can sometimes be a desired, artistic effect known as a crackle glaze.Shivering happens when the glaze doesn't contract as much as the body and it "buckles" or flakes. The end result is a glaze that looks like paint chips peeling away from the clay. This often happens on the pot's edges. In severe cases the glaze is under such compression, it can break the underlying clay body. Shivering can be corrected by adjusting the glaze recipe or the clay recipe or a combination of the two.Understanding how temperature changes clay and glaze is an important part of learning the art of pottery and ceramics. The term "coefficient of expansion" sounds scientific, but it is a principle that has been learned by potters through trial and error over thousands of years. Knowing how to mix your materials to the proper "recipe" can ensure that the coefficients are complementary. This greatly increases the number of successfully fired pieces.Even though your glaze/body coefficients match enough to survive the first test, which is cooling in a kiln, it is important the "marriage" between the body and the glaze can also withstand the heating and cooling cycles it will experience over a lifetime of use. This is why ovenware and ceramics that are "dishwasher safe" have very low coefficients of expansion and the chemical bond between the body and the glaze are precisely formulated.(MORE)
Most people are under the impression the silicon semiconductor is a 20th century invention. Integrated circuits such as those we use today are a product of research which star…ted as far back as 1830. Scientists began looking at a number of individual elements, along with several compounds, which would conduct an electrical current when exposed to light, yet would not conduct when heated. This allowed scientists to control the flow of electricity through these materials. During this period of research, Ferdinand Braun created the world's first non-silicon semiconductor. The Cat's Whisker diode was built from lead sulfide and a galena crystal. This arrangement allowed current to flow easily in one direction but not the other. By 1874, electricity was beginning to dominate the world. It was being used for many things, including the transmission of information via the telegraph and the telephone. By the time the early radio was invented, the term electronics had been coined, and the world would never be the same again. While the integrated circuit was still years in the future, the average "electronic" product was built using a number of vacuum tubes. These tubes were easily damaged, were very unreliable, and produced a lot of heat. They also consumed huge amounts of power to keep them working. Finally, in 1947, Bell Telephone developed an invention which would revolutionize the electronics industry. Their team of experts had developed the world's first transistor, a miniaturized version of the vacuum tube which was rugged, tiny, used very little power, and did not produce massive amounts of heat. Despite the invention of the transistor, the amount of space required to create devices with hundreds of components was still considered to be too much. The US military in particular was looking for ways to further shrink components. This led to the development of the forerunner to the modern integrated circuit, the Micro Module. This device involved creating numbers of individual modules filled with a range of components designed for a specific function. In order to build a complete system, individual modules could simply be plugged into a mainboard. While still far from perfect, this system allowed for fast reliable construction.Kilby had gone to work for Texas Instruments and was working on the development of the Micro Module. Despite its relative success, he was not convinced the device went far enough towards miniaturization to continue being effective. He began the search for a better option, and new materials he could use to shrink the components to a more practical size. In 1958 while most of the research team was away on vacation, Kilby developed the first silicon semiconductor. This first device did nothing more than produce a sine wave which could be seen on an oscilloscope, but with it the integrated circuit would be born. (MORE)
Derivatives are often talked about in the financial news and in the wider media. Despite the widespread use of the term, these financial instruments are rarely explained in de…tail. Though seldom described, derivatives are extremely important, and hundreds of billions of dollars are exchanged buying and selling derivatives every year. Just what are derivatives, and why is it important to understand them?Defined in the broadest possible sense, derivatives are any financial instruments that derive their value from another financial instrument. This sounds somewhat confusing, but when you apply this concept to everyday situations, just what exactly derivatives are starts to make sense. Imagine that the price of corn at your local farmer's market is currently $10 a bushel, but you expect the price of corn to drop soon. With this in mind, you make an agreement with the farmer to buy 12 bushels of corn for $8 a bushel in two weeks regardless of what he is currently charging. An agreement of this sort is a derivative of corn. Specifically, it is a type of derivative called a forward contract.Derivatives are not considered to have any intrinsic value. This means that, taken on their own, derivatives do not possess any value in and of themselves. However, as all investors know, derivatives possess very significant value in financial markets. This is because they derive their value from something with intrinsic value, known as a real-valued asset. Common real-valued assets include stocks, commodities and exchange-traded funds.Theoretically, there are an infinite number of derivatives. The only limit placed on the number of possible types of derivatives is the capacity for human inventiveness. That said, there are two types of derivatives that have the most importance in worldwide financial markets: options and futures. Options are derivatives that give investors the right to buy or sell a real-valued asset for a set price before a certain date. Futures are derivatives that represent an agreement between two investors to buy and sell, respectively, a certain amount of real-valued assets by a certain date.Trading most types of derivatives is not only possible, it is widespread. Options are the most popular type of derivatives for trading with futures a close second. Trading in options requires less of an investment than trading real-valued assets. Options trading also happens much faster than asset trading, making it a good strategy for investors who enjoy making money quickly. Futures are traded in essentially the same way as options, though there are some differences. Two other types of less-common derivatives, forwards and swaps, are sometimes traded, but they are prohibited from trading in federally sanctioned exchanges.Derivatives initially seem like they are entirely in the realm of Wall Street insiders, but these financial instruments are actually quite easy to understand. Though derivatives have no intrinsic value, the value they derive from their underlying assets is often considerable. Investors who focus solely on trading derivatives have the potential to make just as much profit in the market as those who stick to real-valued assets.Options are speculative, risky derivatives. If you correctly predict the future direction of a stock price but the move does not occur before the expiration date of your option, you lose the entire amount of your investment in that option.(MORE)
Semiconductors: When temperature increases, more electrons jump to conduction band from valance bond. Hence resistance decreases.Metals: Already plenty of electrons are there …in conduction band. When temperature increases, the electrons in conduction band of metal vibrate and collide each other during their journey. Hence the the resistance of metal increases with increase of temperature.S.Lakshminarayana(MORE)
No. Semiconductor has negative temp coefficient, because increase in temp causes the increase in the k.e of the electrons bu t not in the no of electrons . these highly energi…sed electronsel increase current, & in terms conductivity.(MORE)
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