Write the formula for the energy stored in the magnetic field of an inductor

\( \newcommand \] Where \(L\) is the inductance in henries, \(\mu\) is the permeability of the core material, \(A\) is the cross sectional area of the coil, \(N\) is the number of coils or turns, \(l\) is the length of the coil. Inductors may also be wound using multiple layers or around a toroidal core, and these designs utilize alternate formulas. Inductor Styles and Packaging Equation \ref\). The three inductors in the center use obvious ferrite cores, two wound on straight cores and the third wound on a toroidal core. The unit to the right uses a high permeability material at the very top and is wrapped in a plastic sheath for protection. Variable inductors are also a possibility and can be made by using a ferrite core that can be slid within the coils, effectively changing the permeability of the core (part ferrite, part air). Figure 9.2.10 : Inductor schematic symbols (top-bottom): standard, variable, iron/ferrite core. The schematic symbols for inductors are shown in Figure 9.2.10 . The standard symbol is at the top. The variable inductor symbol is in the middle and is a twolead device, somewhat reminiscent of the symbol for a rheostat. At the bottom is the symbol for an inductor with an iron, ferrite, or similar high permeability core. In general, like resistors, single inductors are not polarized and cannot be inserted into a circuit backwards. There are, however, special applications where multiple coils can be wound on a common core, and for these, the polarity ...

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:What is the energy is stored in the magnetic field of the inductor after the switch has been in position 1 for a long time, in terms of the quantities given? Write your answer using some or all of the following: R. L. Cand epsilon' for E. Umag = At time t = 0, the switch S is now thrown to connect positions 1 and 2 (connecting the inductor and capacitor and What is the energy is stored in the magnetic field of the inductor after the switch has been in position 1 for a long time, in terms of the quantities given? Write your answer using some or all of the following: R. L. Cand epsilon' for E. Umag = At time t = 0, the switch S is now thrown to connect positions 1 and 2 (connecting the inductor and capacitor and taking the battery out of the circuit). What differential equation does the charge Q satisfy? Before entering the formula for your answer, first write the differential equation in a form satisfying the following criteria: • Write the equation in a form where all of the terms are on one side adding up to zero. • Write the equation in a form where the term containing the highest order derivative is positive. + • Write the equation in a form where the term containing the highest order derivative has a coefficient of 1. R E L For example, if your differential equation contains a second derivat...

[ "article:topic", "Maxwell\u2019s Equations", "flux", "inductor", "torque", "magnetic flux", "Motional Emf", "electromotive force (emf)", "Magnetic Field", "induction", "galvanometer", "Lorentz force", "solenoid", "Faraday\'s law of induction", "Transformer", "Special relativity", "frame of reference", "vector area", "Stoke\'s theorem", "Turbine", "Permeability", "ferromagnet", "showtoc:no", "source@https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-013-electromagnetics-and-applications-spring-2009" ] \( \newcommand\) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Induced EMF The apparatus used by Faraday to demonstrate that magnetic fields can create currents is illustrated in the following figure. When the switch is closed, a magnetic field is produced in the coil on the top part of the iron ring and transmitted (or guided) to the coil on the bottom part of the ring. The galvanometer is used to detect any current induced in a separate coil on the bottom. Faraday’s Apparatus: This is Faraday’s apparatus for demonstrating that a magnetic field can produce a current. A change in the field produced by the top coil induces an EMF and, hence, a current in the bottom coil. When the switch is opened and closed, the galvanometer registers currents in opposite directions. No current flows through the galvanometer when the switch remains closed or open. It was found that each time the switch is closed, the galvanometer detects a curr...

v = L d i d t v = \text L\,\dfrac v\,\text dt + i_0 i = L 1 ​ ∫ 0 T ​ v d t + i 0 ​ i, equals, start fraction, 1, divided by, start text, L, end text, end fraction, integral, start subscript, 0, end subscript, start superscript, T, end superscript, v, start text, d, end text, t, plus, i, start subscript, 0, end subscript L \text L L start text, L, end text is the inductance, a physical property of the inductor. L \text L L start text, L, end text is the scale factor for the relationship between v v v v and d i / d t di/dt d i / d t d, i, slash, d, t . L \text L L start text, L, end text determines how much v v v v gets generated for a given amount of d i / d t di/dt d i / d t d, i, slash, d, t . For real-world resistors, we learned to take care that voltage and current don't get too big for the physical resistor to handle. For real-world inductors, we have to be careful the voltage and change of current don't get too big for the physical inductor to handle. This can be tricky, since it is very easy to create a very big change of current if you open or close a switch. Later on in this article we show how to design for this situation. d i d t = 3 10 × 1 0 − 3 = 300 amperes / sec \dfrac d t d i ​ = 1 0 × 1 0 − 3 3 ​ = 3 0 0 amperes / sec start fraction, d, i, divided by, d, t, end fraction, equals, start fraction, 3, divided by, 10, times, 10, start superscript, minus, 3, end superscript, end fraction, equals, 300, start text, a, m, p, e, r, e, s, end text, slash, start text,...

Energy Stored in an Inductor Energy in an Inductor When a so the energy input to build to a final current i is given by the integral Using the example of a R Nave Energy in Magnetic Field From analysis of the the energy density (energy/volume) is so the energy density stored in the magnetic field is R Nave

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The ability of an electrical conductor, such as coil, to produce induced voltage when the current flowing through it varies is called inductance. To calculate the inductance of a coil based on its physical construction, you can use this equation where: L - Inductance of coil in Henrys (H) N - Number of turns μ r - Permeability of the core μ o - Permeability of air or vacuum (1.26X10 –6) A - Area enclosed l - Coil length Coils of wire manufactured to have a definite value of inductance are called inductors. This equation shows the voltage-current relationship in an inductor where: vis the induced voltage L is the inductance of the inductor di/dt is the instantaneous rate of change of the current through the inductor The induced voltage across an inductor is directly proportional to its inductance and the instantaneous rate of change of the current through the inductor. So the greater the rate of change of current through the coil, the higher is the induced voltage. However, if the current through the inductor doesn’t change at a particular instant, the induced voltage is zero. k - Coefficient of coupling Two coils have mutual inductance when the current in one coil can induce a voltage in the other coil. As you can see in the diagram, if L 1 is connected to a voltage source, though not physically, L 1 and L 2 are linked by a magnetic field. A changing current in L 1 can induce voltage both across L 1 and L 2. If a load is connected across L 2, the induced voltage across L 2...

Learning Objectives By the end of this section, you will be able to: • Explain how energy can be stored in a magnetic field • Derive the equation for energy stored in a coaxial cable given the magnetic energy density The energy of a capacitor is stored in the electric field between its plates. Similarly, an inductor has the capability to store energy, but in its magnetic field. This energy can be found by integrating the magnetic energy density, [latex]nI[/latex] everywhere inside the solenoid. Thus, the energy stored in a solenoid or the magnetic energy density times volume is equivalent to [latex]U=\fracdt,[/latex] so the power absorbed by the inductor is Figure 14.11(a) A coaxial cable is represented here by two hollow, concentric cylindrical conductors along which electric current flows in opposite directions. (b) The magnetic field between the conductors can be found by applying Ampère’s law to the dashed path. (c) The cylindrical shell is used to find the magnetic energy stored in a length l of the cable. Strategy The magnetic field both inside and outside the coaxial cable is determined by Ampère’s law. Based on this magnetic field, we can use Solution Show Answer • We determine the magnetic field between the conductors by applying Ampère’s law to the dashed circular path shown in [latex]B=\frac;[/latex] that is, in the region within the inner cylinder. All the magnetic energy of the cable is therefore stored between the two conductors. Since the energy density of t...