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Induction & Inductance

Computational Modeling of Electromagnetic Systems (F1014B)

Computational Modeling of Electromagnetic Systems

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Recap

  1. Homework
  1. Fundamental Concepts
  • Activity 3 Tuesday 3rd June
  • Webassign 3 Tuesday 3rd June
  • Faraday’s & Lenz Law
  • A changing magnetic field through a loop induces an electromotive force (emf) that can generate a current. (Faraday’s Law)
  • The induced current flows in a direction that opposes the change in magnetic flux that produced it. (Lenz’s Law)

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What is this class about?

  • To review Faraday’s Law and Lenz’s Law to understand how changing magnetic fields induce electric currents.

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  • We will explore the concept of inductance and how circuits can produce self-induced emf.

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Induction

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Induced Current

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Induced Current

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Faraday’s Law

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Faraday’s Law

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Faraday’s Law of Induction

  • Magnetic flux (Φ) measures the amount of magnetic field passing through a surface or loop.�
  • It depends on the strength of the magnetic field (B), the area of the loop (A), and the angle (θ) between the field and the normal to the surface.

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Faraday’s Law of Induction

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Faraday’s Law of Induction

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Lenz’s Law

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Lenz’s Law

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  • In Figure there is a uniform magnetic field through the coil. �
  • The magnitude of the field is increasing, so there is an induced emf.�
  • Using Lenz’s law we could determine the direction of the resulting induced current.

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Lenz’s Law

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Lenz’s Law

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Lenz’s Law

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  • Using Lenz’s law, determine the direction of the current in resistor ab of Fig. when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.

Example

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Faraday’s & Lenz’s Laws

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  • A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig.. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value B0.

Try by yourself!

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Claim a signature for this exercise. �Three signatures = two points on the argumentative exam.

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Applications

  • Electric generators – Convert mechanical energy into electrical energy using rotating coils in magnetic fields (Faraday’s Law).�
  • Transformers – Use changing magnetic flux to transfer electrical energy between circuits at different voltages.�
  • Wireless charging – Inductive coupling transfers energy between coils in chargers and devices like smartphones or electric toothbrushes.�
  • Credit card readers – Use induction to read data encoded in magnetic strips.

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Inductance

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Inductance

  • The current in one wire causes a magnetic field, which exerts a force on the current in the second wire.�
  • What happens when the current is changing?�
  • If the current in coil 1 changes, the flux through coil 2 changes as well; according to Faraday’s law, this induces an emf in coil 2.

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Inductance

  • The efm in the second coil is:���
  • We could define a mutual inductance as:

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Inductance

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Inductance

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  • In one form of Tesla coil (a high-voltage generator popular in science museums), a long solenoid with length l and cross-sectional area A is closely wound with N1 turns of wire. A coil with N2 turns surrounds it at its center. Find the mutual inductance M. Suppose l=0.5m, A=10cm2, N1=1000 and N2=10 turns.

Example

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Self-Inductance

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Inductance

  • A changing current in a circuit produces a changing magnetic flux through the same circuit, which induces an emf in itself - called a self-induced emf.�
  • According to Lenz’s Law, the self-induced emf opposes the change in current that created it.�
  • This opposition makes it harder for the current to change, which is a key principle behind inductors in circuits.

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Inductance

  • We could define the self-inductance L of the circuit as:

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Inductor

  • An inductor is a circuit component designed to have a specific inductance and is symbolized similarly to a coil.�
  • Its main function is to oppose changes in current, making it crucial in circuits.

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Inductance

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  • Determine the self-inductance of a toroidal solenoid with cross-sectional area A and mean radius r, closely wound with N turns of wire on a nonmagnetic core. Assume that B is uniform across a cross section (that is, neglect the variation of B with distance from the toroid axis). Suppose N=200 turns, A=5cm2, r=0.10m.

Try by yourself!

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Claim a signature for this exercise. �Three signatures = two points on the argumentative exam.

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Activity

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Activity 4 is done in pairs. The activity is open until June 10.

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Webassign

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Recommended Video

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Summary

  • Homework
  • Fundamental Concepts
  • Activity 3 Tuesday 3rd June
  • Webassign 3 Tuesday 3rd June
  • Activity 4 Tuesday 10th June
  • Webassign 4 Tuesday 10th June
  • Inductance
  • Reviewed Faraday’s Law and Lenz’s Law, explaining how changing magnetic fields induce electric currents.
  • Introduced the concept of inductance and self-induced emf in circuits.
  • Discussed the function of inductors and explored real-world applications of magnetic induction.

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