self-inductance

Examples of self-inductance in the following topics:

• Inductance

  • Self-inductance, the effect of Faraday's law of induction of a device on itself, also exists.
  • where L is the self-inductance of the device.
  • A device that exhibits significant self-inductance is called an inductor, and given the symbol in .
  • Units of self-inductance are henries (H) just as for mutual inductance.
  • The self-inductance of a solenoid of cross-sectional area A and length ℓ is

• Inductance

  • The answer is yes, and that physical quantity is called inductance.
  • The larger the mutual inductance M, the more effective the coupling.
  • Self-inductance, the effect of Faraday's law of induction of a device on itself, also exists.
  • where L is the self-inductance of the device.
  • A device that exhibits significant self-inductance is called an inductor.

• RL Circuits

  • Recall that induction is the process in which an emf is induced by changing magnetic flux.
  • Mutual inductance is the effect of Faraday's law of induction for one device upon another, while self-inductance is the the effect of Faraday's law of induction of a device on itself.
  • An inductor is a device or circuit component that exhibits self-inductance.
  • The characteristic time $\tau$ depends on only two factors, the inductance L and the resistance R.
  • The greater the inductance L, the greater it is, which makes sense since a large inductance is very effective in opposing change.

• Reasoning

  • We use many mental shortcuts when conducting inductive, deductive, abductive, and analogous reasoning to find a solution to a problem.
  • It is also closely identified with the ability to self-consciously change beliefs, attitudes, traditions, and institutions, and therefore indicates the capacity for freedom and self-determination.
  • In order to solve problems, we utilize four major forms of reasoning: deduction, induction, abduction, and analogy.
  • However, unlike deduction, induction, or abduction where at least one premise (or the conclusion) is general, analogy concerns itself only with specifics and particulars.
  • Differentiate between the processes of induction, deduction, abduction, and analogy, discussing heuristics that are used in these processes

• Logic

  • Francis Bacon (1561-1626) is credited with formalizing inductive reasoning.
  • "Bacon did for inductive logic what Aristotle did for the theory of the syllogism.
  • Statistical inference is an application of the inductive method.
  • While inductive methods are useful, there are pitfalls to avoid.
  • Abduction is similar to induction.

• Back EMF, Eddy Currents, and Magnetic Damping

  • Back EMF, eddy currents, and magnetic damping are all due to induced EMF and can be explained by Faraday's law of induction.
  • When the coil of a motor is turned, magnetic flux changes, and an electromotive force (EMF), consistent with Faraday's law of induction, is induced.
  • Lenz' law tells us the induced EMF opposes any change, so that the input EMF that powers the motor will be opposed by the motor's self-generated EMF, called the back EMF of the motor.

• Regulating Immune Tolerance

  • Immune tolerance of self and harmless antigens occurs by deleting B and T cells that recognize those antigens, often near mucosal surfaces.
  • Processed antigens displayed on APCs are detected by T cells in the MALT and at various mucosal induction sites, such as the tonsils, adenoids, appendix, or the mesenteric lymph nodes of the intestine.
  • The primary mechanism for developing immune tolerance to self-antigens occurs during the selection for weakly, self-binding cells during T and B lymphocyte maturation.
  • Any T or B lymphocytes that recognize harmless foreign or "self" antigens are deleted before they can fully mature into immunocompetent cells.
  • There are populations of T cells that suppress the immune response to self-antigens.

• Faraday's Law of Induction and Lenz' Law

  • This relationship is known as Faraday's law of induction.
  • The minus sign in Faraday's law of induction is very important.
  • As the change begins, the law says induction opposes and, thus, slows the change.
  • This is one aspect of Lenz's law—induction opposes any change in flux.
  • Express the Faraday’s law of induction in a form of equation

• Proof by Mathematical Induction

  • Proving an infinite sequence of statements is necessary for proof by induction, a rigorous form of deductive reasoning.
  • The assumption in the inductive step that the statement holds for some $n$, is called the induction hypothesis (or inductive hypothesis).
  • To perform the inductive step, one assumes the induction hypothesis and then uses this assumption to prove the statement for $n+1$.
  • This completes the induction step.
  • Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes.

• Sequences of Mathematical Statements

  • Sequences of statements are logical, ordered groups of statements that are important for mathematical induction.
  • Sequences of statements are necessary for mathematical induction.
  • Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers.
  • For example, in the context of mathematical induction, a sequence of statements usually involves an algebraic statement into which you can substitute any natural number $(0, 1, 2, 3, ...)$ and the statement should hold true.
  • This concept will be expanded on in the following module, which introduces proof by mathematical induction.