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Chapter 9: 9.37P (page 433)

A microwave antenna radiating at 10GHz is to be protected from the environment by a plastic shield of dielectric constant 2.5. What is the minimum thickness of this shielding that will allow perfect transmission (assuming normal incidence)? [Hint: Use Eq. 9. 199.]

Short Answer

Expert verified

The minimum thickness of the shielding is 9.5 mm.

Step by step solution

01

Expression for the minimum thicknesof the shielding:

Write the expression for minimum thickness.

d=蟺k ........(1)

02

Determine the minimum thickness of the shielding

Substitute k=蝇vand 蝇=2蟺谓in equation (1).

d=蟺蝇谓d=蟺2蟺谓vd=v2谓

Substitute 谓=cnand n=蔚渭蔚0渭0in the above expression.

d=cn2谓d=c2谓蔚渭蔚0渭0 ....... (2)

Here, 渭鈮�渭0and 蔚蔚0=蔚T.

Substitute 渭鈮�渭0and 蔚蔚0=蔚Tin equation (2).

d=c2谓蔚T........(3)

Substitute c=3脳108m/s,谓=10GHzand蔚T=2.5 in equation (3).

d=3脳108m/s2脳10GHZ脳109Hz1GHz2.5d=9.49脳10-3m脳103mm1md=9.5mm

Therefore, the minimum thickness of the shielding is 9.5 mm.

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Most popular questions from this chapter

(a) Suppose you imbedded some free charge in a piece of glass. About how long would it take for the charge to flow to the surface?

(b) Silver is an excellent conductor, but it鈥檚 expensive. Suppose you were designing a microwave experiment to operate at a frequency of1010Hz. How thick would you make the silver coatings?

(c) Find the wavelength and propagation speed in copper for radio waves at role="math" localid="1655716459863" 1MHz. Compare the corresponding values in air (or vacuum).

Suppose

E(r,胃,蠒,t)=Asin胃r[cos(kr-蝇t)-1krsin(kr-蝇t)]蠒铃�

(This is, incidentally, the simplest possible spherical wave. For notational convenience, let(kr-蝇t)鈮�uin your calculations.)

(a) Show that Eobeys all four of Maxwell's equations, in vacuum, and find the associated magnetic field.

(b) Calculate the Poynting vector. Average S over a full cycle to get the intensity vector . (Does it point in the expected direction? Does it fall off like r-2, as it should?)

(c) Integrate over a spherical surface to determine the total power radiated. [Answer:4蟺A2/3渭0c]

Show that the modeTE00 cannot occur in a rectangular wave guide. [Hint: In this case蝇c=k , so Eqs. 9.180 are indeterminate, and you must go back to Eq. 9.179. Show that is a constant, and hence鈥攁pplying Faraday鈥檚 law in integral form to a cross section鈥攖hatBz=0 , so this would be a TEM mode.]

Suppose

E(r,胃,蠒,t)=A蝉颈苍胃r[cos(kr鈭�蝇t)鈭�(1/kr)sin(kr鈭�蝇t)]蠒^

(This is, incidentally, the simplest possible spherical wave. For notational convenience, let role="math" localid="1658817164296" (kr鈭�蝇t)鈮�u in your calculations.)

(a) Show that E obeys all four of Maxwell's equations, in vacuum, and find the associated magnetic field.

(b) Calculate the Poynting vector. Average S over a full cycle to get the intensity vector I. (Does it point in the expected direction? Does it fall off liker鈭�2, as it should?)

(c) Integrate role="math" localid="1658817283737" I鈰�da over a spherical surface to determine the total power radiated. [Answer: 4蟺础2/3渭0c ]

Calculate the reflection coefficient for light at an air-to-silver interface (渭1=渭2=渭0,蔚=蔚0,蟽=6脳107鈥�(惟m)-1)at optical frequencies(蝇=4脳1015/s).
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