Boundary Condition | Washington State University

University:
Washington State University
Course:
Physics 103 | Problem Solving for Physics 101
Academic year:

2020
Views:

283

Pages:

3
Author:

Janor

Boundary Conditions:-Z=0 orx-y plane(Z<0)(z > 0 ) mediummediumE,= =Et,+EN,E2=Etz+EN2D, =14+DN,B2 =DtztDN2->H1=Ht,+HN,H2=Ht2+H2N2B,=Bt,+BN,B2=B+ist2N2^IfE = A ax + Bay + Cazthen for Z=O boundaryEt = Aax + By is The tengential to Z=O Surface^EN = Caz is the Normal to 1=0 Surface.Boundary is a surface whose thickness tends to zeroBoundary conditions give the relation between fieldof mediumI& medium2( Boundary Seperatesmedium I & medium 2 ).If fields of one medium are given then usingboundary conditions we can find fields of othermedium. There are Four general boundary conditions.1.The tangential components of electric field intensities arecontinous (equal) at the boundary Surface Mathematicaly.Et, = EtzEE, / = Etz2. The normal components of electric flux densities arediscontinous ( not equal) at the boundary Surface By anamount equal to the Surface charge density (Ps) anthe boundary Surface.Mathematicaly:DN,1-DN2=Psc/m2c/m2c/m2#If P==/DNi/ =/DN2/DNI=N2E, EN, = t2 EN23 The tengential components of magnetic field intensities are discontinousat the boundary surface by an amount equal to The surfacecurrent density (R) present can the boundary surfaceMathematicaly^Ht,-Ht2=AN12XK(A/mA/mA/m# If K=O then Ftt, = Ht2A#aN2 : It is a normal unit vector to the boundarySurface from medium 1 to medium2 4. The normal components of magnetic flux densities areContinous at the boundary surface.BN, = BN2# u HN, = le2 HN2Observations:Ifz=0J2 = T2 E2 & E2 = = 0Z000mediummedium2Ez=0Conductor b2 wE=Etz++EN,=02yo0Now . Boundary condition - ii => Et, = Etz= = 0Boundary condi from is =) 1DNI - DN2/ = PsPull /ENZ/ = ls=>IDN,1 = lsNote i Between dielectric medium1and conductor medium2boundary surfaceE1,=0DNI = PsE1 EN, = Ps2On the conductor surface electric field is minimum[ Et, =0 (min) and magnetic field is maximum mum [He, 70 (man)

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