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Peter Apps
Daniella Garcia-Loos
Peter Apps
Daniella Garcia-Loos
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?
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.
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 (ΦB) 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.
Image Courtesy of electricalacademia
B is the magnetic field strength, A is the area we're measuring the flux through, and θ 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)
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:
Faraday's law of induction is a principle in physics that describes the relationship between a changing magnetic field and the electric current induced in a conductor. It states that the induced electromotive force (emf) in a conductor is equal to the rate of change of the magnetic flux through the conductor.
Here are some key points about Faraday's law of induction:
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 (ℓ) 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:
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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).
Lenz's law is a principle in physics that describes the direction of the induced current in a conductor. It states that the induced current will always act to oppose the change in the magnetic field that caused it.
Here are some key points about Lenz's law:
** 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:
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