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Chapter 32 Maxwell’s Equations

Understanding Maxwell's equations, including Gauss' law for magnetic fields and the Ampere-Maxwell law, which relate changing electric flux to induced magnetic fields. Learn how to treat a changing electric field as a displacement current. Differential form of Maxwell's equations.

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Chapter 32 Maxwell’s Equations

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  1. Chapter 32 Maxwell’s Equations James Clerk Maxwell, 1831-1879

  2. Gauss’ Law for Magnetic Fields: The law asserts that the net magnetic flux FBthrough any closed Gaussian surface is zero. Here B is the magnetic field.

  3. Induced Magnetic Fields: Here B is the magnetic field induced along a closed loop by the changing electric flux FEin the region encircled by that loop.

  4. Induced Magnetic Fields: Ampere Maxwell Law: Here iencis the current encircled by the closed loop. In a more complete form, : the displacement current : the displacement current density

  5. Example, Magnetic Field Induced by Changing Electric Field:

  6. Example, Magnetic Field Induced by Changing Electric Field, cont.:

  7. Example, Treating a Changing Electric Field as a Displacement Current:

  8. Maxwell’s Equations:

  9. Maxwell’s Equations: Differential form

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