lecture17 - Physics 2102 Magnetic fields produced by...

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Unformatted text preview: Physics 2102 Magnetic fields produced by currents Physics 2102 Gabriela González The Biot-Savart Law • Quantitative rule for computing the magnetic field from any electric current • Choose a differential element of wire of length dL and carrying a current i • The field d B from this element at a point located by the vector r is given by the Biot-Savart Law: L d r 3 4 r r L id B d × = π μ i μ 0 =4 π x10-7 T.m/A (permeability constant) Jean-Baptiste Biot (1774-1862) ? Felix Savart (1791-1841) Compare with: 3 1 4 dqr dE r πε = Biot-Savart Law • An infinitely long straight wire carries a current i . • Determine the magnetic field generated at a point located at a perpendicular distance R from the wire. • Choose an element d s as shown • Biot-Savart Law: d B ~ d s x r points INTO the page • Integrate over all such elements 3 4 r r s id B d × = π μ 3 ) sin ( 4 r r ids dB θ π μ = ∫ ∞ ∞- = 3 ) sin ( 4 r r ds i B θ π μ ( 29 ∫ ∞ ∞- + = 2 / 3 2 2 4 R s Rds i π μ ( 29 ∫ ∞ + = 2 / 3 2 2 2 R s Rds i π μ ( 29 ∞ + = 2 / 1 2 2 2 2 R s R s iR π μ R i π μ 2 = r...
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

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lecture17 - Physics 2102 Magnetic fields produced by...

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