Arghya M.

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Physics (Electricity and Magnetism)

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Question:

What is an electromagnetic field?

Arghya M.

Answer:

the electromagnetic field sometimes referred to as an EM field, is generated when charged particles, such as electrons, are accelerated. All electrically charged particles are surrounded by electric fields. Charged particles in motion produce magnetic fields. When the velocity of a charged particle changes, an EM field is produced. Electromagnetic fields were first discovered in the 19th century, when physicists noticed that electric arcs (sparks) could be reproduced at a distance, with no connecting wires in between. This led scientists to believe that it was possible to communicate over long distances without wires. The first radio transmitters made use of electric arcs. These "spark transmitters" and the associated receivers were as exciting to people in the early 20th century as the Internet is today. This was the beginning of what we now call wireless communication. Electromagnetic fields are typically generated by alternating current (AC) in electrical conductors. The frequency of the AC can range from one cycle in thousands of years (at the low extreme) to trillions or quadrillions of cycles per second( at the high extreme). The standard unit of EM frequency is the hertz, abbreviated Hz.Larger units are often used. A frequency of 1,000 Hz is one kilohertz(kHz); a frequency of 1,000 kHz is one megahertz (MHz); a frequency of 1,000 MHz is one gigahertz (GHz). The wavelength of an EM field is related to the frequency. If the frequency f of an EM wave is specified in megahertz and the wavelength w is specified in meters (m), then in free space, the two are related according to the formula w = 300/f For example, a signal at 100 MHz (in the middle of the American FM broadcast band) has a wavelength of 3 m or about 10 feet. This same formula applies if the frequency misgiven in gigahertz and the wavelength is specified in millimeters (mm). Thus, a signal at 30 GHz would have a wavelength of 10 mm or a little less than half an inch. The realm of EM field energy is called the electromagnetic radiation spectrum. In theory, this extends from arbitrarily long wavelengths to arbitrarily short wavelengths, or, as engineers sometimes imprecisely quip, "from DC to light."

Calculus

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Question:

What is inequality in integrals?

Arghya M.

Answer:

A number of general inequalities hold for Riemann-integrable functions defined on a closed and bounded interval [a, b] and can be generalized to other notions of integral (Lebesgue and Daniell). Upper and lower bounds. An integrable function f on [a, b], is necessarily bounded on that interval. Thus there are real numbers m and M so that m ≤ f (x) ≤ M for all x in [a, b]. Since the lower and upper sums of f over [a, b] are therefore bounded by, respectively, m(b − a) and M(b − a), it follows that m ( b − a ) ≤ ∫ a b f ( x ) d x ≤ M ( b − a ) . {\displaystyle m(b-a)\leq \int _{a}^{b}f(x)\,dx\leq M(b-a).} m(b-a)\leq \int _{a}^{b}f(x)\,dx\leq M(b-a). Inequalities between functions. If f(x) ≤ g(x) for each x in [a, b] then each of the upper and lower sums of f is bounded above by the upper and lower sums, respectively, of g. Thus ∫ a b f ( x ) d x ≤ ∫ a b g ( x ) d x . {\displaystyle \int _{a}^{b}f(x)\,dx\leq \int _{a}^{b}g(x)\,dx.} \int _{a}^{b}f(x)\,dx\leq \int _{a}^{b}g(x)\,dx. This is a generalization of the above inequalities, as M(b − a) is the integral of the constant function with value M over [a, b]. In addition, if the inequality between functions is strict, then the inequality between integrals is also strict. That is, if f(x) < g(x) for each x in [a, b], then ∫ a b f ( x ) d x < ∫ a b g ( x ) d x . {\displaystyle \int _{a}^{b}f(x)\,dx<\int _{a}^{b}g(x)\,dx.} \int _{a}^{b}f(x)\,dx<\int _{a}^{b}g(x)\,dx. Subintervals. If [c, d] is a subinterval of [a, b] and f(x) is non-negative for all x, then ∫ c d f ( x ) d x ≤ ∫ a b f ( x ) d x . {\displaystyle \int _{c}^{d}f(x)\,dx\leq \int _{a}^{b}f(x)\,dx.} \int _{c}^{d}f(x)\,dx\leq \int _{a}^{b}f(x)\,dx. Products and absolute values of functions. If f and g are two functions, then we may consider their pointwise products and powers, and absolute values: ( f g ) ( x ) = f ( x ) g ( x ) , f 2 ( x ) = ( f ( x ) ) 2 , | f | ( x ) = | f ( x ) | . {\displaystyle (fg)(x)=f(x)g(x),\;f^{2}(x)=(f(x))^{2},\;|f|(x)=|f(x)|.\,} (fg)(x)=f(x)g(x),\;f^{2}(x)=(f(x))^{2},\;|f|(x)=|f(x)|.\, If f is Riemann-integrable on [a, b] then the same is true for |f|, and | ∫ a b f ( x ) d x | ≤ ∫ a b | f ( x ) | d x . {\displaystyle \left|\int _{a}^{b}f(x)\,dx\right|\leq \int _{a}^{b}|f(x)|\,dx.} \left|\int _{a}^{b}f(x)\,dx\right|\leq \int _{a}^{b}|f(x)|\,dx. Moreover, if f and g are both Riemann-integrable then fg is also Riemann-integrable, and ( ∫ a b ( f g ) ( x ) d x ) 2 ≤ ( ∫ a b f ( x ) 2 d x ) ( ∫ a b g ( x ) 2 d x ) . {\displaystyle \left(\int _{a}^{b}(fg)(x)\,dx\right)^{2}\leq \left(\int _{a}^{b}f(x)^{2}\,dx\right)\left(\int _{a}^{b}g(x)^{2}\,dx\right).} \left(\int _{a}^{b}(fg)(x)\,dx\right)^{2}\leq \left(\int _{a}^{b}f(x)^{2}\,dx\right)\left(\int _{a}^{b}g(x)^{2}\,dx\right). This inequality, known as the Cauchy–Schwarz inequality, plays a prominent role in Hilbert space theory, where the left-hand side is interpreted as the inner product of two square-integrable functions f and g on the interval [a, b]. Hölder's inequality. Suppose that p and q are two real numbers, 1 ≤ p, q ≤ ∞ with 1/p + 1/q = 1, and f and g are two Riemann-integrable functions. Then the functions |f|p and |g|q are also integrable and the following Hölder's inequality holds: A

Electrical Engineering

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Question:

How does a Synchronous Machine work?

Arghya M.

Answer:

The synchronous machine has a 3 phase stator winding wound around it. Again, in the rotor , there is simple dc winding. In the case of the synchronous motor, stator is excited by 3 phase ac supply and the rotor is excited with dc supply. Now, the 3 phase winding is wound around the rotor where each phase winding is mutually displaced by 120 degrees in space coordinates. When stator winding is supplied by ac source, a rotating magnetic field is created. Now, the rotor is excited by dc supply so that a constant magnitude magnetic field is created. Next, the rotor is moved by the prime mover and speeded up to the synchronous speed (The speed of stator magnetic field). Hence we can see, the relative velocity of stator and rotor field is zero. So a constant torque is created by this two interacting magnetic field which balances the counter torque of mechanical load. This is how asynchronous motor works.

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