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# chp38_8 - A uniform electric field is confined to a...

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PHY2061 R. D. Field Department of Physics chp38_8.doc University of Florida Electric & Magnetic Fields that Change with Time Changing Magnetic Field Produces an Electric Field: A uniform magnetic field is confined to a circular region of radius, r , and is increasing with time . What is the direction and magnitude of the induced electric field at the radius r? Answer: If I choose my orientation to be counterclockwise then Φ B = B(t)A with A = π r 2 . Faraday’s Law of Induction tells us that r r E dl rE r d dt r dB dt B Circle = = − = − 2 2 π π ( ) Φ , and hence E(r) = -(r/2) dB/dt . Since dB/dt > 0 ( increasing with time ), E is negative which means that it points opposite my chosen orientation. Changing Electric Field Produces a Magnetic Field:
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Unformatted text preview: A uniform electric field is confined to a circular region of radius, r , and is increasing with time. What is the direction and magnitude of the induced magnetic field at the radius r? Answer: If I choose my orientation to be counterclockwise then Φ E = E(t)A with A = π r 2 . Ampere’s Law ( with J = 0 ) tells us that r r B dl rB r d dt r c dE dt E Circle ⋅ = = = ∫ 2 2 2 πε µ π ( ) Φ , and hence B(r) = (r/2c 2 ) dE/dt . Since dE/dt > 0 ( increasing with time ), B is positive which means that it points in the direction of my chosen orientation. B-out increasing with time r E E-out increasing with time r B...
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