Ampere's Law - PHY 2049C General Physics B Today: 1)...

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PHY 2049C – General Physics B Today: 1) Ampere's Law 2) Induction
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Gauss' (Non-)Law for Magnetism Electric Field: The number of field lines crossing a closed surface is proportional to the amount of charge inside of the surface. Magnetic Field: The number of field lines crossing a closed surface is zero. “There are no magnetic charges” 0 inside E S Q Ed A ε Φ= = G G 0 B S Bd A = G G
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Ampére's Law for Magnetism The Integral of the tangential component of the Magnetic Field around a closed curve equals μ 0 times the current going through the enclosed Area C This looks a lot like Gauss' law, only different ! z Good for symmetric situations: Find curve, along which B t is constant z Circumference * B t = μ 0 I C 0 C C B dl I μ ⋅= G G
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Example for Ampére's Law How strong is the magnetic field around a long straight current ? The current going through the area of the closed path is “just the total current” I R Closed Path C 0 0 0 2 2 C C C C B dl I B RI I B R μ πμ π ⋅= = = G G
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Example 2: Ampére's Law Toroid field What is the magnetic Field on the outside / inside Here, there is no net current penetrating the area, every winding goes in and comes out again. Therefore, the magnetic field outside the coil is zero. (The same on the inside: B=0) Closed Path (outside coil)
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Example 2: Ampére's Law Toroid field Here, coil is wound around a ring core. What is the magnetic Field at the center of that ring ? The current penetrates the area once on every winding !
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Ampere's Law - PHY 2049C General Physics B Today: 1)...

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