For more information, please see full course syllabus of AP Physics C: Electricity & Magnetism

For more information, please see full course syllabus of AP Physics C: Electricity & Magnetism

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### Maxwell's Equations

- Gauss’s Law allows you to find the electric field in situations of spherical, cylindrical, and planar symmetry.
- Gauss’s Law for Magnetism states that the total magnetic flux through any closed surface is zero, and is a direct outcome to the finding that there are no magnetic monopoles.
- Faraday’s Law allows you to find the inducted emf due to a changing magnetic flux.
- Ampere’s Law allows us to calculate the magnetic field due to an electric current as well as a changing electric field. The contribution due to the penetrating current is known as the conduction current, and the contribution due to the changing electric field is known as the displacement current.

### Maxwell's Equations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Objectives 0:07
- Maxwell's Equations 0:19
- Gauss's Law
- Gauss's Law for Magnetism
- Faraday's Law
- Ampere's Law
- Revising Ampere's Law 1:49
- Allows Us to Calculate the Magnetic Field Due to an Electric Current
- Changing Electric Field Produces a Magnetic Field
- Conduction Current
- Displacement Current
- Maxwell's Equations (Complete) 2:58

### AP Physics C: Electricity and Magnetism Online Course

I. Electricity | ||
---|---|---|

Electric Charge & Coulomb's Law | 30:48 | |

Electric Fields | 1:19:22 | |

Gauss's Law | 52:53 | |

Electric Potential & Electric Potential Energy | 1:14:03 | |

Electric Potential Due to Continuous Charge Distributions | 1:01:28 | |

Conductors | 20:35 | |

Capacitors | 41:23 | |

II. Current Electricity | ||

Current & Resistance | 17:59 | |

Circuits I: Series Circuits | 29:08 | |

Circuits II: Parallel Circuits | 39:09 | |

RC Circuits: Steady State | 34:03 | |

RC Circuits: Transient Analysis | 1:01:07 | |

III. Magnetism | ||

Magnets | 8:38 | |

Moving Charges In Magnetic Fields | 29:07 | |

Forces on Current-Carrying Wires | 17:52 | |

Magnetic Fields Due to Current-Carrying Wires | 24:43 | |

The Biot-Savart Law | 21:50 | |

Ampere's Law | 26:31 | |

Magnetic Flux | 7:24 | |

Faraday's Law & Lenz's Law | 1:04:33 | |

IV. Inductance, RL Circuits, and LC Circuits | ||

Inductance | 6:41 | |

RL Circuits | 42:17 | |

LC Circuits | 9:47 | |

V. Maxwell's Equations | ||

Maxwell's Equations | 3:38 | |

VI. Sample AP Exams | ||

1998 AP Practice Exam: Multiple Choice Questions | 32:33 | |

1998 AP Practice Exam: Free Response Questions | 29:55 |

### Transcription: Maxwell's Equations

*Hello, everyone, and welcome back to www.educator.com.*0000

*In this lesson, we are just going to review Maxwell’s equations.*0004

*Our objectives include making sure students are familiar with these equation so they can associate each equation with its implications.*0008

*Let us take a look at Maxwell’s equations as we define them so far.*0015

*First we have Gauss’s law, the integral / the closed surface E ⋅ DA is the total close charge divided by ε₀.*0021

*This was very useful, although it is always true, it is mostly useful*0030

*when you are looking for the electric field indications where you have some sort of symmetry.*0034

*Symmetry typically being planar, cylindrical, or spherical.*0040

*Gauss’s law for magnetism, the integral / the close surface of B ⋅ DA = 0.*0044

*It was another way of stating that magnetic monopoles do not exist.*0050

*Any closed surface whatever magnetic field lines go in, the same amount of magnetic field lines come out.*0054

*Faraday's law, the integral / the closed loop of E ⋅ DL = - D/ DT the derivative/ the open surface of B ⋅ DA,*0061

*this is really the magnetic flux.*0070

*When we have no change in magnetic flux, this simplified down to Kirchhoff’s voltage law.*0072

*Ampere’s law, we said the integral / the closed loop of B ⋅ DL = μ₀ I.*0079

*We use this to find the magnetic field in situations of symmetry that was a much more elegant than*0085

*when we used the more challenging Biot-Savart law.*0092

*We put the asterisk here, there was more that we had to talk about it.*0096

*By the way, that is penetrating current.*0100

*There is a little bit more to ampere’s law and that is what we are going to develop next.*0104

*Ampere’s law as written, allows us to calculate the magnetic field due to some electric current that penetrates our Amperian loop.*0109

*However, we also know that the change in electric field produces a magnetic field and we have not taken that into account yet.*0117

*That piece looks like this, the integral/ the closed loop of B ⋅ DL is the permeability × the permittivity × the time rate of change of the electric flux.*0124

*Or if you wanted to expand out our electric flux, μ₀ ε₀ × the derivative of and*0136

*there is our electric flux, integral / the open surface of E ⋅ DA.*0141

*That is the piece that we have not thrown into the equation yet, even though we know it exists.*0147

*How do we put all that together?*0152

*To combine the effects, we are going to take a look at the contribution due to the penetrating current*0155

*which we are going to call conduction current.*0161

*The contribution due to the changing electric field, the changing electric flux, and that is what we called the displacement current.*0164

*Putting all of those together to come up with a refined version of Ampere’s law, our final Maxwell's equation looks like this.*0172

*Gauss’s law for magnetism, faraday’s law, and Ampere’s law, now the integral / the closed loop of B ⋅ DL = μ₀ I penetrating,*0183

*our conduction current piece + our displacement current piece μ₀ ε₀ × the derivative of the electric flux.*0194

*That is our complete Maxwell’s equations and that completes the basic content of the course for E & M AP Physics C.*0205

*Thank you so much for watching www.educator.com.*0214

*Make it a great day everybody.*0217

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