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# tsl243 - I ~ B Â d ~ â€˜ = B(2 Ï€r â€¢ 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 Â· d ~ â€˜ = B (2 Ï€r ) . â€¢ Fraction of current inside loop: I C I = Ï€r 2 Ï€R 2 . â€¢ Magnetic field at radius r < R : B = Î¼ I C 2 Ï€r = Î¼ Ir 2 Ï€R 2 . â€¢ B increases linearly with r from zero at the center. â€¢ Magnetic field at the perimeter: B = Î¼ I 2 Ï€R . tsl243 â€“ p.1/1...
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