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Lesson_4.5_Printable_PPT

# Lesson_4.5_Printable_PPT - Maxwells Equations and...

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Maxwell’s Equations and Electromagnetic Waves According to Gauss’s law for electric fields, the net electric flux leaving or entering a closed surface enclosing a charge Q is given by: o Q E dA ε = Here ε o is the permittivity of free space and it has a value 8.85 × 10 -12 C 2 .N -1 .m -2 This is Maxwell’s first equation.

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Maxwell’s second equation is a similar statement for the magnetic field. Since there are no free magnetic monopoles, a given space cannot enclose any magnetic monopoles. The amount of magnetic flux entering a closed surface must be equal to the flux leaving it. Therefore the net flux out of the enclosed volume is zero leading to the equation: The first two Maxwell’s equations, given above, are for integrals of the electric and magnetic fields over closed surfaces enclosing a volume. 0 B dA =
The third and fourth of Maxwell’s equations are for integrals of electric and magnetic fields around closed curves. We take the component of the field pointing along the curve and calculating the line integral and calculate Edl or Bdl and integrate it along the length of the curve. These line integrals represent the work that would be needed to take a charge around a closed curve in an electric field, and a magnetic monopole (if one existed!) around a closed curve in a magnetic field. The simplest version of Maxwell’s third equation is the electrostatic case: 0 E dl =

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A similar line integral in a magnetic field is the Ampere’s law. Ampere's Law states that for any closed loop path, the sum The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source. of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.
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