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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=πk ........(1)

02

Determine the minimum thickness of the shielding

Substitute k=ωvand ω=2πνin equation (1).

d=πωνd=π2πνvd=v2ν

Substitute ν=cnand n=εμε0μ0in the above expression.

d=cn2νd=c2νεμε0μ0 ....... (2)

Here, μμ0and εε0=εT.

Substitute μμ0and εε0=εTin equation (2).

d=c2νεT........(3)

Substitute c=3×108m/s,ν=10GHzandεT=2.5 in equation (3).

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

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

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