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: XJBrrrr+=×∇0µ. Solution: tJXBJ∂∂−=⋅∇−×∇=ρrrrrrr0011tXBJ∂∂−=⋅∇−×∇⋅∇=⋅∇rrrrrrr0011Thus, tX∂∂=⋅∇0rrbut Err⋅∇=0εso that ∂∂⋅∇=⋅∇∂∂=⋅∇tEEtXrrrrrr0000)(and hence tEX∂∂=rr00and tEJB∂∂+=×∇rrrr000Corrected Ampere&s Law (integral form): ∫∫∫
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.