Electromagnetic Fields.pdf

# E are the two governing fundamental differential

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E are the two governing fundamental differential equations for electrostatics in any medium. v is the volume density of free charges From equation (X), v v vdv Ddv 0 or using Gauss’ law s Q ds D …… Generalized Gauss’ law Gauss law states that the total outward flux of the electric displacement (or simply, the total outward electric flux) over any closed surface is equal to the total free charge enclosed in the surface. For a linear and isotropic dielectric medium, E X P E P e o where X e is the electric susceptibility. A dielectric medium is linear if Xe is independent of E and is homogenous if Xe is independent of space coordinate. But P E D o E E E e o e o o 1

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28 E E r o where e r 1 is the relative permittivity of a dielectric constant of a medium, and r o is the absolute permittivity. The maximum electric field intensity that a dielectric material air withstands without breakdown is the dielectric strength of the material. 2.2.5 BOUNDARY CONDITIONS FOR ELECTROSTATIC FIELDS ∆h ∆w b a d c E 1 E 2 ∆h D 1 a n2 a n1 D 2 ∆s Medium 2 Medium1 Fig.13Electrostatic Fields at the boundary of dielectric media w cd ba h ad bc 0 Contribution of the line integral of E along abcda is w E w E dl E abcda 2 1 As 0 h i.e. E 1 and E 2 at equipotential 0 2 1 w E w E t t t t E E 2 1 : The tangential component of an E-field is continuous across an interface E D or D E 2 2 1 1 t t D D
29 As 0 h , v vdv dv D as s s s ds D s a D a D ds D s n n 1 2 2 1 but 1 2 n n a a s D D a s s s D D a s a D a D n n n n 2 1 2 2 1 2 2 2 2 1 Or s D D n n 2 1 i.e. the normal component of D field is discontinuous across an interface where a surface charge exists: the amount of discontinuity being equal to the surface charge density. If there are no free charges at the interface, 0 s as n n D D 2 1 or n n E E E E 2 2 1 1 2.2.6 CAPACITANCES AND CAPACITORS The charge of a conducting body Q, is directly proportional to its potential V. i.e. Q ∞ V CV Q or F V Q C where C is the capacitance of the isolated conducting body . For two parallel plate capacitor, V 12 being the potential difference between the two conductors, F V Q C 12 To determine the capacitance C between two conductors, 1. Choose an appropriate coordinate system for the given geometry.

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• Fall '19
• Magnetic Field

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