WEBVTT physics/ap-physics-c-electricity-magnetism/fullerton
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Hello, everyone, and welcome back to www.educator.com.
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In this lesson, we are just going to review Maxwell’s equations.
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Our objectives include making sure students are familiar with these equation so they can associate each equation with its implications.
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Let us take a look at Maxwell’s equations as we define them so far.
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First we have Gauss’s law, the integral / the closed surface E ⋅ DA is the total close charge divided by ε₀.
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This was very useful, although it is always true, it is mostly useful
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when you are looking for the electric field indications where you have some sort of symmetry.
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Symmetry typically being planar, cylindrical, or spherical.
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Gauss’s law for magnetism, the integral / the close surface of B ⋅ DA = 0.
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It was another way of stating that magnetic monopoles do not exist.
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Any closed surface whatever magnetic field lines go in, the same amount of magnetic field lines come out.
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Faraday's law, the integral / the closed loop of E ⋅ DL = - D/ DT the derivative/ the open surface of B ⋅ DA,
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this is really the magnetic flux.
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When we have no change in magnetic flux, this simplified down to Kirchhoff’s voltage law.
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Ampere’s law, we said the integral / the closed loop of B ⋅ DL = μ₀ I.
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We use this to find the magnetic field in situations of symmetry that was a much more elegant than
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when we used the more challenging Biot-Savart law.
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We put the asterisk here, there was more that we had to talk about it.
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By the way, that is penetrating current.
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There is a little bit more to ampere’s law and that is what we are going to develop next.
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Ampere’s law as written, allows us to calculate the magnetic field due to some electric current that penetrates our Amperian loop.
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However, we also know that the change in electric field produces a magnetic field and we have not taken that into account yet.
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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.
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Or if you wanted to expand out our electric flux, μ₀ ε₀ × the derivative of and
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there is our electric flux, integral / the open surface of E ⋅ DA.
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That is the piece that we have not thrown into the equation yet, even though we know it exists.
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How do we put all that together?
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To combine the effects, we are going to take a look at the contribution due to the penetrating current
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which we are going to call conduction current.
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The contribution due to the changing electric field, the changing electric flux, and that is what we called the displacement current.
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Putting all of those together to come up with a refined version of Ampere’s law, our final Maxwell's equation looks like this.
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Gauss’s law for magnetism, faraday’s law, and Ampere’s law, now the integral / the closed loop of B ⋅ DL = μ₀ I penetrating,
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our conduction current piece + our displacement current piece μ₀ ε₀ × the derivative of the electric flux.
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That is our complete Maxwell’s equations and that completes the basic content of the course for E & M AP Physics C.
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Thank you so much for watching www.educator.com.
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Make it a great day everybody.