mutual inductance
(noun)
The ratio of the voltage in a circuit to the change in current in a neighboring circuit.
Examples of mutual inductance in the following topics:
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Inductance
- where M is defined to be the mutual inductance between the two devices.
- The larger the mutual inductance M, the more effective the coupling.
- A large mutual inductance M may or may not be desirable.
- We want a transformer to have a large mutual inductance.
- Units of self-inductance are henries (H) just as for mutual inductance.
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Inductance
- Mutual inductance is the effect of Faraday's law of induction for one device upon another, such as the primary coil in transmitting energy to the secondary in a transformer.
- where M is defined to be the mutual inductance between the two devices.
- The larger the mutual inductance M, the more effective the coupling.
- Transformers run backward with the same effectiveness, or mutual inductance M.
- Their mutual inductance M indicates the effectiveness of the coupling between them.
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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.
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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.
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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
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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.
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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.
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Different Lines of Reasoning
- Apply two different lines of reasoning—inductive and deductive—to consciously make sense of observations and reason with the audience.
- One important aspect of inductive reasoning is associative reasoning: seeing or noticing similarity among the different events or objects that you observe.
- Here is a statistical syllogism to illustrate inductive reasoning:
- The conclusion of an inductive argument follows with some degree of probability.
- In order to engage in inductive reasoning, we must observe, see similarities, and make associationsbetween conceptual entities.
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Changing Magnetic Flux Produces an Electric Field
- Faraday's law of induction states that changing magnetic field produces an electric field: $\varepsilon = -\frac{\partial \Phi_B}{\partial t}$.
- We have studied Faraday's law of induction in previous atoms.
- In a nutshell, the law states that changing magnetic field $(\frac{d \Phi_B}{dt})$ produces an electric field $(\varepsilon)$, Faraday's law of induction is expressed as $\varepsilon = -\frac{\partial \Phi_B}{\partial t}$, where $\varepsilon$ is induced EMF and $\Phi_B$ is magnetic flux.
- Therefore, we get an alternative form of the Faraday's law of induction: $\nabla \times \vec E = - \frac{\partial \vec B}{\partial t}$.This is also called a differential form of the Faraday's law.
- Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field.
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Reasoning and Inference
- Scientists use inductive reasoning to create theories and hypotheses.
- An example of inductive reasoning is, "The sun has risen every morning so far; therefore, the sun rises every morning."
- A faulty example of inductive reasoning is, "I saw two brown cats; therefore, the cats in this neighborhood are brown."
- As you can see, inductive reasoning can lead to erroneous conclusions.
- Can you distinguish between his deductive (general to specific) and inductive (specific to general) reasoning?