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Unformatted text preview: s summarized by the following formula:
+ ∇. = − .
(iii) In the time harmonic electromagnetic field, field vectors that vary with space coordinates and
are sinusoidal functions of time can similarly be represented by vector phasors that depend on
spacecoordinates but not on time.
(a)
1
= .   [cos(2
2 + ) + cos( + − )]( (b)
= 1 (×) 1
2 = [ × (iv)
′
= = = . . On the surface of the wire
= = =
= .
× (2 = . =− ) 2 2 (v) ρ H
E × ) Q3)
(i) Four Maxwell’s equations are consistent. They are not all independent. That’s mean the two
divergence equations can be derived from the two curl equations, by making use of the equation of
continuity.
(ii) The 4 fundamental field vectors E,D,B,H represent twelve unknowns, because this each having
three components . so twelve scalar equations are required for the determination of these 12
unknowns.
The required equations are supplied by the two vector curl equations and the two vector
constitutive relations = and = , each vector equation being equivalent to three scalar equations.
(iii) (a) ∇ ×
∇× =− ; =. =− (c) ∇ × = + Let = 0 in dielectric medium so, ∇ × = ; ∇× =
=. (iv)
∇× =− We can represent H from the component of directions,
components of directions such as , , ∇× (a) Three scalar equations are,
−. = − −. = − −. = − = , , . Also E can represent the (b) ∇ × =. . = − . = − . = −...
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 Spring '13
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