Consider a wedge that is 30 cm long and 8 cm thick. Wedge's attenuation is 0.3 /cm. Derive the equation and calculate the average transmission through this wedge. **Problem Statement:**Consider a wedge that is 30 cm long and 8 cm thick. The wedge's attenuation is 0.3 per cm. Derive the equation and calculate the average transmission through this wedge.**Diagram Explanation:**The diagram shows a right-angled wedge with the length (base) of 30 cm and the height (thickness) of 8 cm. The vertical arrows represent the incoming rays that will pass through the wedge.**Calculation:**1. The wedge causes attenuation to any ray passing through it, described by the attenuation coefficient, which is given as 0.3 per cm.2. To compute the transmission, consider a differential element at a distance "x" along the length of the wedge. The thickness "t" at this point is given by the relation: \[ t(x) = \frac{8}{30}x = \frac{4}{15}x \]3. The intensity "I(x)" of a ray passing through a thickness "t(x)" is governed by the exponential attenuation law: \[ I(x) = I_0 e^{-0.3 \cdot t(x)} \] Where \(I_0\) is the initial intensity of the ray.4. Substitute \(t(x)\) into the equation: \[ I(x) = I_0 e^{-0.3 \cdot \left(\frac{4}{15}x\right)} \]5. Average transmission can be computed by integrating \(I(x)\) over the range 0 to 30 cm and dividing by the total length: \[ \text{Average Transmission} = \frac{1}{30} \int_{0}^{30} e^{-0.08x} \, dx \]6. Solving this integral: \[ \int e^{-0.08x} \, dx = -\frac{1}{0.08} e^{-0.08x} = -12.5 e^{-0.08x} \]7. Evaluate from 0 to 30: \[ \left[-12.5 e^{-0.08x}\right]_{0}^{30} = -12.5 \left(e^{-2.4} - 1\right) \]8. Calculate: \[ =

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Answered: Consider a wedge that is 30 cm long and…

Consider a wedge that is 30 cm long and 8 cm thick. Wedge's attenuation is 0.3 /cm. Derive the equation and calculate the average transmission through this wedge.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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