Boundary condition Conductor freespace Electric boundary condition Maxwells
Boundary condition
Conductor freespace Electric boundary condition Maxwell’s equations for time varying field 1 4 Unit-4 3 Current continuity equation Conductor dielcrtic Dielectric dielectric 2 Magnetic boundary condition
Conductor –free space boundary conditions Free space X Y Conductor
conductor Boundary between conductor & free space Free space I
Boundary between conductor & free space conductor Free space EN I a. N a. T
Human wave
a. Z=a. N a. Y =a. T=aρ X Free space conductor
Conductor-dielectric boundary condition dielectric Conductor
dielectric conductor
dielectric-dielectric boundary condition dielectric
Boundary between dielectric & dielectric E 1 E 2 a. N a. T
dielectric
Magnetic Boundary condition
Magnetic boundary condition μ 1 H H H μ 2
Boundary condition for Medium 1 Medium 2
a. N Current sheet between medium 1 & medium 2 ai a. N a a. T a. N 12 Medium 1 b I a. T a. N 12 d Medium 2 c Boundary surface
a. N a a. T ai a. N 12 Medium 1 b I a. T a. N 12 d Medium 2 c Boundary surface
The Continuity Equation d. I ds Arbitrary volume V Q d. I Idl d. I
The Continuity Equation d. I ds Arbitrary volume V Q d. I
The continuity equation The current density diverges at a point , then charge density at that point decreases with time at the rate equal to divergence of current density
Maxwell’s Equations for time varying fields
Animation makes it clear Plane of propagation Antenna wire
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I 5 A 3 A 2 A 0 -2 A -3 A -5 A
Maxwell’s III equation 7/28/2010(2 u 1/2 u 2) Ms, B. P. Harne
I 1=2 A Q=80 c ρv 1=4 c/m 2 Time t 1 I 1=4 A Q=100 c ρv 2=6 c/m 2 Time t 2
I Maxwell’s IV equation I I=I(wt 1) 7/28/2010(2 u 1/2 u 2) I=I(wt 2) Ms, B. P. Harne
Maxwell’s I equation 7/28/2010(2 u 1/2 u 2) I Ms, B. P. Harne
source of steady magnetic field 1. permanent magnet, 2. a direct current 3. electric field changing with time.
Maxwell’s II equation 7/28/2010(2 u 1/2 u 2) I Ms, B. P. Harne
Conduction to Displacement Current Ratio (Cont’d) • We have • Therefore 44
Conduction to Displacement Current Ratio • The value of the quantity s/we at a specified frequency determines the properties of the medium at that given frequency. • In a metallic conductor, the displacement current is negligible below optical frequencies. • In free space (or other perfect dielectric), the conduction current is zero and only displacement current can exist. 45
Maxwell’s equations for steady field Point form Integral form
Maxwell’s equations for time varying field Point form Integral form
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