tsl243 - I ~ B d ~ ‘ = B(2 πr • Fraction of current...

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Ampère’s Law: Magnetic Field Inside a Wire Consider a long, straight wire of radius R . The current is I distributed uniformly over the cross section. Apply Ampère’s law, I ~ B · d ~ = μ 0 I C , to the circular loop of radius r < R . The symmetry dictates that the magnetic field ~ B is directed tangentially with magnitude B depending on R only. Line integral:
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Unformatted text preview: I ~ B · d ~ ‘ = B (2 πr ) . • Fraction of current inside loop: I C I = πr 2 πR 2 . • Magnetic field at radius r < R : B = μ I C 2 πr = μ Ir 2 πR 2 . • B increases linearly with r from zero at the center. • Magnetic field at the perimeter: B = μ I 2 πR . tsl243 – p.1/1...
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