Find what you need to study
6 min read•january 8, 2023
Daniella Garcia-Loos
Peter Apps
Daniella Garcia-Loos
Peter Apps
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?
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 (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.
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:
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 through the conductor.
Here are some key points about :
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 causes an induced EMF. Looking at our definition of flux, we see that the can be changed in 3 main ways:
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?). In the simplest sense, Lenz's Law says that the induced EMF in a loop or wire will always oppose the change in that caused it.
The basic reasoning for this comes from the Law of . 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:
Ok, now let's take a look at a bunch of examples:
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.
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?
What is the induced EMF in the wire?
The loop of wire has a resistance of R. What is the value of the induced current?
Counterclockwise, Use the Right Hand Rule
ε = Bℓv
I = ε / R = Bℓv / R
Conservation of Energy
: Conservation of energy is a fundamental principle stating that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another. In other words, the total amount of energy in a closed system remains constant over time.Electromagnetic Induction
: Electromagnetic induction is the process of generating an electric current in a conductor by changing the magnetic field around it. It involves the interaction between electricity and magnetism.Faraday's Law of Induction
: Faraday's Law of Induction states that a change in magnetic field induces an electromotive force (emf) in a closed loop, resulting in the generation of an electric current. In simpler terms, it explains how moving magnets or changing magnetic fields can create electricity.Magnetic Flux
: Magnetic flux refers to the measure of the total magnetic field passing through a given area. It depends on the strength of the magnetic field, the angle between the magnetic field and the area, and the size of the area.Right-Hand Rule
: The right-hand rule is a method used to determine the direction of a magnetic field, current, or force in relation to each other. It states that if you point your thumb in the direction of the current, and curl your fingers around it, your fingers will point in the direction of the magnetic field.Weber (Wb)
: Weber (Wb) is the SI unit used to measure magnetic flux.6 min read•january 8, 2023
Daniella Garcia-Loos
Peter Apps
Daniella Garcia-Loos
Peter Apps
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?
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 (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.
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:
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 through the conductor.
Here are some key points about :
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 causes an induced EMF. Looking at our definition of flux, we see that the can be changed in 3 main ways:
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?). In the simplest sense, Lenz's Law says that the induced EMF in a loop or wire will always oppose the change in that caused it.
The basic reasoning for this comes from the Law of . 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:
Ok, now let's take a look at a bunch of examples:
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.
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?
What is the induced EMF in the wire?
The loop of wire has a resistance of R. What is the value of the induced current?
Counterclockwise, Use the Right Hand Rule
ε = Bℓv
I = ε / R = Bℓv / R
Conservation of Energy
: Conservation of energy is a fundamental principle stating that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another. In other words, the total amount of energy in a closed system remains constant over time.Electromagnetic Induction
: Electromagnetic induction is the process of generating an electric current in a conductor by changing the magnetic field around it. It involves the interaction between electricity and magnetism.Faraday's Law of Induction
: Faraday's Law of Induction states that a change in magnetic field induces an electromotive force (emf) in a closed loop, resulting in the generation of an electric current. In simpler terms, it explains how moving magnets or changing magnetic fields can create electricity.Magnetic Flux
: Magnetic flux refers to the measure of the total magnetic field passing through a given area. It depends on the strength of the magnetic field, the angle between the magnetic field and the area, and the size of the area.Right-Hand Rule
: The right-hand rule is a method used to determine the direction of a magnetic field, current, or force in relation to each other. It states that if you point your thumb in the direction of the current, and curl your fingers around it, your fingers will point in the direction of the magnetic field.Weber (Wb)
: Weber (Wb) is the SI unit used to measure magnetic flux.© 2024 Fiveable Inc. All rights reserved.
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