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Lecture 8: Faraday's Law of Induction
February 18, 2025
Reading Assignment
- Read: 27.1-27.3, 27.6 (through p. 537)
- Study: Eqs 27.1a, 27.1b, 27.2; Exs 27.3, 27.5, 27.10
- Ignore: “Diamagnetism” in Section 27.6 (p. 538).
Objectives
- (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday “real life” situations.
- For a given simple magnetic field and a surface, calculate the magnetic flux.
- Given a situation in which there is a changing magnetic flux, apply Faraday's law to relate the emf, current, or circulation of the \(\vec{E}\)-field to the properties of the magnetic field and of the coil.
- Distinguish situations for which there is or is not an induced emf.
- Apply Lenz's Law to determine the direction of induced emf, electrical currents, eddy currents, magnetic fields, or forces.
Homework
- Wednesday's Assigned Problems: A23, A24, A25; Ch. 27: 1, 2, 11, 13, 28, 37, 47
- Monday's Hand-In Problems relevant to today's lecture: A28; Ch. 27: 14, 40, 46, 48
Lecture Materials
- Click here for the Lecture overheads.Answers: CT1a - 2, CT1b - 1, CT1c - 1, CT1d - 1, CT1e - 2; CT2a - 1, CT2b - 2, CT2c - 1, CT2d - 1; CT3 - 2; CT4 - 4; CT5 - 2
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Example #1: Determining the emf in a loop near a long wire with a current that drops to 0 in a specified time interval. Lenz's Law in here as well as Faraday.
- Example #2: Determining the emf in a loop moving into a region with magnetic field.
Pre-Class Entertainment
- Old Man - Neil Young
- Peace Train - Cat Stevens
- Casey Jones - Grateful Dead
- Be OK - Ingrid Michaelson
- Good People - Jack Johnson
Assigned Problems Guide
- A23: medium. A Faraday's law problem where you are calculating $\Delta\Phi_B/\Delta t$, much like the example we did in lecture.
- A24: medium. As the problem is titled, it's a Faraday's law problem where you need to take a derivative with respect to time to find the EMF.
- A25: quick. Think about energy.
- 27-1: quick Lenz's law problem, like the Concept Tests we did in class.
- 27-2: medium. When the switch is closed, the current must go from 0 to some nonzero steady value. Focus first on that transition time while the current is increasing.
- 27-11: medium-quick. Just calculate the magnetic flux from the information given. No laws of electricity and magnetism involved on this one.
- 27-13: medium. It's a “backwards” problem: start with Ohm's law to find the EMF and then go to Faraday's law. Note: you are finding $dB/dt$.
- 27-28: tricky. Use that EMF = $\oint\vec E\cdot d\vec l$ to solve it like an Ampere's law problem, except for $E$ instead of $B$. Instead of current encircled, on the right hand side we want changing magnetic flux encircled.
- 27-37: medium-long. Classical Faraday's law problem. Find the EMF from the changing magnetic field, and then find the current. Part (b) is just a different way of specifying which time you want.
- 27-47: medium-long. For a rotating coil, the angle $\theta = \omega t$, and you'll be taking a time derivative of $\cos(\omega t)$ to find the EMF. Note that sine has a max value of 1, so the max value of the EMF will be whatever is multiplying the sine.