๐Ÿ“š

All Subjects

ย >ย 

๐Ÿงฒย 

AP Physics 2

ย >ย 

๐Ÿงฒ

Unit 5

5.3 Electromagnetic Induction

4 min readโ€ขnovember 28, 2020

peter57616

Peter Apps


AP Physics 2ย ๐Ÿงฒ

Bookmarkedย 681ย โ€ขย 61ย resources
See Units

Electromagnetic Induction

Making Magnets from Electricity ๐Ÿง™

Electromagnetic Induction is the process of using magnetic fields to produce a voltage. If that voltage is produced in a complete circuit, it can create a current. We've seen in the previous section that current moving through a wire creates a magnetic field, all we're doing here is reversing that process.
Take a few minutes to play around with this PhET simulation, especially the Pickup Coil Tab. What does it take to make the bulb light up?
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-77Igdgap8DLT.gif?alt=media&token=7c433554-4611-4fd8-b066-a32439b7a5a1

Image created by the author using PhET

The magnet needs to be moving! Just like we needed a moving charge to create a magnetic field, we need a moving magnetic field to induce a potential difference.

Magnetic Flux ๐ŸŒ

Flux is a very useful concept to help describe a wide variety of physics concepts. We're going to apply it here for magnetic fields, and if you take AP C: E&M we'll also use it to describe electric fields. Basically, flux describes how much of something goes through a given area.
We're going to imagine an area on the surface of a magnetized object. It doesn't matter what the object is. The magnetic flux (ฮฆB) is then described by how many magnetic field lines pass through the area. Generally, we define the area to be parallel to the magnetic field, since this simplifies the math. However, if we can't do that, we take the dot product between the area vector and the magnetic field to determine the flux.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-AnBYmwXrOfYX.png?alt=media&token=31f8a3ee-a243-40fe-9fa6-4767d55ef2b4

Image Courtesy of electricalacademia

B is the magnetic field strength, A is the area we're measuring the flux through, and ฮธ is the angle between the magnetic field vector and the area vector. Looking at the units for the flux, we can see that it would be Tm^2, which is equivalent to a Weber (Wb)

Creating EMF

Since we know that a moving magnet causes a potential difference to appear in the simulation, we can attempt to model that mathematically. This can be done using Faraday's Law:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-PxXAnL8scFsV.png?alt=media&token=2b496e38-7a88-4426-b4ba-79acd41a88d0
Typically, you'll use the first section of the equation if you're asked generically about the scenario, the last section is if you're calculating the EMF in a loop of wire (โ„“) is the length of the loop and v is the velocity at which the loop is moving. For a more in-depth dive into where this equation comes from, check out the AP Physics C: EM Guide on this topic.
The change in magnetic flux causes an induced EMF. Looking at our definition of flux, we see that the magnetic flux can be changed in 3 main ways:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-8syyqdyrVvGH.png?alt=media&token=c6501ae4-e74f-4f28-ada0-fc8cd9b5728f

Resources:

Image Courtesy of physics.stackexchange

What about the Direction of the EMF?

Lenz's Law deals with the negative sign in Faraday's Law. It gives us the direction of the induced EMF and lets us find the direction of the induced current, as well (you do remember the Right-Hand Rule, right?). In the simplest sense, Lenz's Law says that the induced EMF in a loop or wire will always oppose the change in magnetic flux that caused it.
The basic reasoning for this comes from the Law of Conservation of Energy. If the induced EMF was in the same direction as the flux, we would enter a positive feedback loop that would produce infinite EMF (and infinite energy).
For some simple DIY examples of Lenz's Law in action, check out this video by D!NG, or this one by Veritasium.
Ok, now let's take a look at a bunch of examples:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-MO1gBzYykNZR.png?alt=media&token=5b10e0e7-9f47-43d5-9182-0be322523409

Image Courtesy of wikipedia

  • In case (a) the magnet is stationary. There is no changing flux, so there is no current or opposing induced magnetic field.
  • Case (b) shows the magnet falling. The flux is increasing because the magnetic field B1 is getting stronger, so there must be an induced magnetic force that opposes it B2 pointing upwards. Using the RHR, we can see that the induced current in the loop must be traveling CCW to produce this opposing field.
  • Case (c) shows the reverse of case (b). The flux is decreasing because the magnet is moving away, so the induced magnetic field must be pointing in the same direction as B1 to counteract the weakening field. This induced field is created by the current traveling in a CW direction.

Practice Problems

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Frg186IOVcuJ.png?alt=media&token=12c41f40-be0b-4202-a855-5cfb2e9b38ec

Image created by the author

  1. A loop of conducting wire with length L and width W is entering a magnetic field B at velocity v. What direction will the induced current travel in?
  2. What is the induced EMF in the wire?
  3. The loop of wire has a resistance of R. What is the value of the induced current?

Answers

  1. Counterclockwise, Use the Right Hand Rule
  2. ฮต = Bโ„“v
  3. I = ฮต / R = Bโ„“v / R

Was this guide helpful?

Join us on Discord
Thousands of students are studying with us for the AP Physics 2 exam.
join now
Hours Logo
Studying with Hours = the ultimate focus mode
Start a free study session
๐Ÿ” Are you ready for college apps?
Take this quiz and find out!
Start Quiz
Browse Study Guides By Unit
๐Ÿ“†Big Reviews: Finals & Exam Prep
โœ๏ธBlogs
๐Ÿ’งUnit 1: Fluids
๐Ÿ”ฅUnit 2: Thermodynamics
โšก๏ธUnit 3: Electric Force, Field, and Potential
๐Ÿ’กUnit 4: Electric Circuits
๐ŸงฒUnit 5: Magnetism and Electromagnetic Induction
๐Ÿ”Unit 6: Geometric and Physical Optics
โš›๏ธUnit 7: Quantum, Atomic, and Nuclear Physics
Get your free AP physics 2 survival pack
Instant access to every resource you need to get a 5
Join us on Discord
Thousands of students are studying with us for the AP Physics 2 exam.
join now
Hours Logo
Studying with Hours = the ultimate focus mode
Start a free study session
๐Ÿ“ฑ Stressed or struggling and need to talk to someone?
Talk to a trained counselor for free. It's 100% anonymous.
Text FIVEABLE to 741741 to get started.
ยฉ 2021 Fiveable, Inc.