MAGNETIC FIELDS DUE TO CURRENTS

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PHY110W MAGNETISM MAGNETIC FIELDS DUE TO CURRENTS MAGNETIC FIELD DUE TO CURRENT IN A LONG, STRAIGHT WIRE d s i s θ R r × dB P Using symmetry (every current element ds in the upper half of the wire has a corresponding element in the lower half causing the same field at P), the magnitude of the magnetic field at point P due to a long, straight, current-carrying wire is ∞ 0i 2 4 µ B = sinθ ds π ∫ (30-7) 2 r 0 = ° − = R , and r where sinθ sin( 180 θ) ∴ B = µ 0i 2π ∞ ∫ 0 R ( 2 2) s + R 32 ds 2 2 r = s + R ∞ µ 0i ⎡ s ⎤ ∴ B = 12 2π R ⎢( 2 2 s R ) ⎥ ⎣ + ⎦0 µ 0i ∴ B = (30-6) 2π R The direction of B is given by the RH curled fingers rule. 14
PHY110W MAGNETISM MAGNETIC FIELDS DUE TO CURRENTS THE MAGNETIC FIELD AROUND A LONG, STRAIGHT, CURRENT-CARRYING WIRE i B r The force a current-carrying wire experiences in an external magnetic field is therefore due to the superpositioning of the two magnetic fields: N S … N F S 15
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MAGNETIC FIELDS DUE TO CURRENTS

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