tsl243 - I ~ B d ~ = B (2 r ) . Fraction of current inside...

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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 r ) . Fraction of current inside loop: I C I = r 2 R 2 . Magnetic field at radius r &lt; R : B = I C 2 r = Ir 2 R 2 . B increases linearly with r from zero at the center. Magnetic field at the perimeter: B = I 2 R . tsl243 p.1/1...
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