Homework13 - Homework 13 Answers 95.657 Fall 2011...

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Dr. Christopher S. Baird, UMass Lowell Problem 1 Using the same approach as in class, derive what Maxwell's equations would look like if there were real magnetic charges as well as real electric charges. SOLUTION If there were magnetic charges, then these charges could also move to create magnetic charge currents. Then these charges and currents would have to obey a magnetic charge continuity equation: ∂ magnetic t =∇⋅ J magnetic Magnetic charges would than give rise to diverging total magnetic B fields in the same way that total electric charges give rise to diverging electric fields: ∇⋅ B = magnetic Plugging this into the continuity equation would yield: −∇⋅ B t =∇⋅ J magnetic We can always add zero to an equation. Let us add the mathematical statement ∇⋅∇× E = 0 −∇⋅ B t −∇⋅∇× E =∇⋅ J magnetic We integrate away the divergence operator on both sides of the equation and rearrange ∇× E =− J magnetic B t In summary, if there were magnetic monopoles, Maxwell's equations would become: ∇⋅ E = total,electric 0 , ∇⋅ B
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This note was uploaded on 02/13/2012 for the course PHYSICS 95.657 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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Homework13 - Homework 13 Answers 95.657 Fall 2011...

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