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Page 1: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The concept of line and surface integrals
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The Maxwell Equations in Vacuum
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Their version in integral form
Page 2: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The First Maxwell Eq.
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Page 3: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The Second Maxwell Eq.
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The Second Maxwell Eq.
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Page 4: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The Third Maxwell Eq.
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Page 5: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Page 6: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The Fourth Maxwell Eq.
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Current enclosed by the loop G
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Ampere's law
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Maxwell noticed this law was incomplete
Page 7: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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James Clerk Maxwell noticed that Ampere's law could lead to contradictory results. Consider, for example, the case of an alternating current across a capacitor: On one hand, one obtains
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On the other hand,
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Parallel plates capacitor
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wire
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Mathematical surface S1
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Loop G (a circumference of radius R)
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Loop G (a circumference of radius R)
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Mathematical surface S2
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Current crossing the surface S1
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Current crossing the surface S2
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Page 8: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Page 9: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Integral along the loop G
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Integral across the surfa- ce S
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Current crossing the surface S
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Fourth Maxwell's equation (1873)
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Returning to our example, let's see how the 4th Maxwell Eq. lift the contradiction. First, lets find the magnetic field B using the loop G (shown in the figure) and the surface S1
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Page 10: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Page 11: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Page 12: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 13: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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B. The Maxwell Equations in Differential Form
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The remaining pages ARE NOT part of PH-213
Page 14: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 15: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Reference: R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 (Differential Calculus of Vector Fields;) Chapte 3 (Vector Integral Calculus.
Page 16: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The Gauss' theorem
Page 17: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 18: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Reference: R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 3 (Section 3-3 The Gauss theorem.)
Page 19: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 20: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 21: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 22: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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The Stoke's Theorem
Page 23: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 24: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
Page 25: rTheir version in integral form - pdx.edu R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 2 \(Differential Calculus of Vector Fields;\) Chapte 3 \(Vector Integral
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Reference: R. Feynman, " The Feynman Lectures on Physics," Vol-II , Chapter 3 (Section 3-6 The Stokes theorem.)
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