# chp38_4 - PHY2061 R D Field Finding the Missing...

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PHY2061 R. D. Field Department of Physics chp38_4.doc University of Florida Finding the Missing Term ( differential method ) Must make Ampere°s Law consistent with charge conservation. Look for the missing piece as follows: X J B r r r r + = × 0 µ . Solution: t J X B J = × = ρ µ µ r r r r r r 0 0 1 1 t X B J = × = ρ µ µ r r r r r r r 0 0 1 1 Thus, t X = ρ µ 0 r r but E r r = 0 ε ρ so that = = t E E t X r r r r r r 0 0 0 0 ) ( ε µ ε µ and hence t E X = r r 0 0 ε µ and t E J B + = × r r r r 0 0 0 ε µ µ Corrected Ampere°s Law (integral form):
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