Problem 7.2 Write general expressions for the electric and magnetic ...

brothersroocooElectronics - Devices

Oct 18, 2013 (3 years and 10 months ago)

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Problem 7.2
Write general expressions for the electric and magnetic elds of a
1-GHz sinusoidal plane wave traveling in the +y-direction in a lossless nonmagnetic
medium with relative permittivity

r
= 9.The electric eld is polarized along the
x-direction,its peak value is 6 V/m,and its intensity is 4 V/mat t =0 and y =2 cm.
Solution:
For f =1 GHz,

r
=1,and

r
=9,

=2

f =2

×10
9
rad/s,
k =
2


=
2


0


r
=
2

f
c


r
=
2

×10
9
3×10
8

9 =20

rad/m,
E(y,t) = x6cos(2

×10
9
t −20

y+

0
) (V/m).
At t =0 and y =2 cm,E =4 V/m:
4 =6cos(−20

×2×10
−2
+

0
) =6cos(−0.4

+

0
).
Hence,

0
−0.4

=cos
−1
µ
4
6

=0.84 rad,
which gives

0
=2.1 rad =120.19

and
E(y,t) = x 6cos(2

×10
9
t −20

y+120.19

) (V/m).