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