Chapter 9: Q37P (page 433)

A microwave antenna radiating at $10 G H z$ 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 $9.5 m m .$

Step by step solution

Expression for the minimum thickness of the shielding:

Write the expression for minimum thickness

$d = \frac{π}{k}$ …… (1)

Determine the minimum thickness of the shielding:

Substitute $k = \frac{ω}{v}$ and $ω = 2 π v$ in equation (1).

$d = \frac{π}{(\frac{ω}{v})}$

$d = \frac{π}{(\frac{2 π v}{v})}$

$d = \frac{v}{2 v}$

Substitute $v = \frac{c}{n}$ and $n = \sqrt{\frac{ε μ}{ε_{0} μ_{0}}}$ in the above expression.

$d = \frac{(\frac{c}{n})}{2 v}$

$d = \frac{c}{2 v \sqrt{\frac{ε μ}{ε_{0} μ_{0}}}}$ …… (2)

Here, $μ \approx μ_{0} and \sqrt{\frac{ε}{ε_{0}}} = \sqrt{ε_{r}} .$

Substitute $μ \approx μ_{0}$ and $\sqrt{\frac{ε}{ε_{0}}} = \sqrt{ε_{r}}$ in equation (2).

$d = \frac{c}{2 ν \sqrt{ε_{r}}}$

Substitutelocalid="1657471538175" $= 3 \times 10^{8} m / s, = 10 G H z$ , and $ε_{r} = 2.5$ in equation (3).

$d = \frac{3 \times 10^{8} m / s}{2 (10 GHz \times \frac{10^{9} Hz}{1 GHz}) \sqrt{2.5}}$

localid="1657471850034" $d = 9.49 \times 10^{- 3} m \times (\frac{10^{3} mm}{1 m}) d = 9.5 mm$

Therefore, the minimum thickness of the shielding is $9.5 m m$ .

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A microwave antenna radiating at $10 G H z$ 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

Step by step solution

Expression for the minimum thickness of the shielding:

Determine the minimum thickness of the shielding:

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A microwave antenna radiating at 10 GHzis to be protected from the environment by a plastic shield of dielectric constant2.5. . What is the minimum thickness of this shielding that will allow perfect transmission (assuming normal incidence)? [Hint: Use Eq. 9.199.]

Short Answer

Step by step solution

Expression for the minimum thickness of the shielding:

Determine the minimum thickness of the shielding:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Kinematics Physics

Quantum Physics

Modern Physics

Oscillations

Translational Dynamics

Study anywhere. Anytime. Across all devices.

A microwave antenna radiating at $10 G H z$ 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.]