Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

5.3 Electromagnetic Induction

6 min readjanuary 8, 2023

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Electromagnetic Induction

Making Magnets from Electricity

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

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.

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 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)

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

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 :

  • is a fundamental principle in electromagnetism and is used to understand and analyze the behavior of induced currents in electrical and electronic circuits. It is a useful tool for predicting the behavior of electrical and electronic devices and circuits.
  • is based on the principle that a changing magnetic field will induce an electromotive force (emf) in a conductor. The induced emf is equal to the rate of change of the through the conductor. This relationship is described by the equation emf = -N*dΦ/dt, where emf is the induced emf, N is the number of turns in the conductor, Φ is the , and t is time.
  • is often used in conjunction with Lenz's law, which states that the induced current will always act to oppose the change in the magnetic field that caused it. Together, these laws describe the behavior of induced currents in electrical and electronic circuits.
  • is a key principle in the operation of generators, transformers, and other electrical and electronic devices that rely on induced currents. It is also used to understand and analyze the behavior of electromagnetic waves and to predict the behavior of electrical and electronic circuits.
  • is a consequence of the and the fact that energy can be converted from one form to another. It is based on the observation that a changing magnetic field can induce an electric current in a conductor.

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:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-8syyqdyrVvGH.png?alt=media&token=c6501ae4-e74f-4f28-ada0-fc8cd9b5728f

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?). 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:

  • Lenz's law is a consequence of the and the fact that energy can be converted from one form to another.
  • Lenz's law is used to understand and analyze the behavior of induced currents in electrical and electronic circuits. It is a useful tool for predicting the behavior of electrical and electronic devices and circuits.
  • Lenz's law is based on the principle that the induced current will always act to oppose the change in the magnetic field that caused it. This means that the induced current will always act to reduce or eliminate the change in the magnetic field.
  • Lenz's law can be used to predict the direction of the induced current in a conductor and to design and troubleshoot electrical and electronic circuits.
  • Lenz's law is often used in conjunction with , which states that the magnitude of the induced current is proportional to the rate of change of the magnetic field. Together, these laws describe the behavior of induced currents in electrical and electronic circuits.

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. ε = Bℓv

  3. I = ε / R = Bℓv / R

Key Terms to Review (6)

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.

5.3 Electromagnetic Induction

6 min readjanuary 8, 2023

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Electromagnetic Induction

Making Magnets from Electricity

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

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.

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 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)

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

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 :

  • is a fundamental principle in electromagnetism and is used to understand and analyze the behavior of induced currents in electrical and electronic circuits. It is a useful tool for predicting the behavior of electrical and electronic devices and circuits.
  • is based on the principle that a changing magnetic field will induce an electromotive force (emf) in a conductor. The induced emf is equal to the rate of change of the through the conductor. This relationship is described by the equation emf = -N*dΦ/dt, where emf is the induced emf, N is the number of turns in the conductor, Φ is the , and t is time.
  • is often used in conjunction with Lenz's law, which states that the induced current will always act to oppose the change in the magnetic field that caused it. Together, these laws describe the behavior of induced currents in electrical and electronic circuits.
  • is a key principle in the operation of generators, transformers, and other electrical and electronic devices that rely on induced currents. It is also used to understand and analyze the behavior of electromagnetic waves and to predict the behavior of electrical and electronic circuits.
  • is a consequence of the and the fact that energy can be converted from one form to another. It is based on the observation that a changing magnetic field can induce an electric current in a conductor.

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:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-8syyqdyrVvGH.png?alt=media&token=c6501ae4-e74f-4f28-ada0-fc8cd9b5728f

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?). 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:

  • Lenz's law is a consequence of the and the fact that energy can be converted from one form to another.
  • Lenz's law is used to understand and analyze the behavior of induced currents in electrical and electronic circuits. It is a useful tool for predicting the behavior of electrical and electronic devices and circuits.
  • Lenz's law is based on the principle that the induced current will always act to oppose the change in the magnetic field that caused it. This means that the induced current will always act to reduce or eliminate the change in the magnetic field.
  • Lenz's law can be used to predict the direction of the induced current in a conductor and to design and troubleshoot electrical and electronic circuits.
  • Lenz's law is often used in conjunction with , which states that the magnitude of the induced current is proportional to the rate of change of the magnetic field. Together, these laws describe the behavior of induced currents in electrical and electronic circuits.

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. ε = Bℓv

  3. I = ε / R = Bℓv / R

Key Terms to Review (6)

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.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.