Explanation 1) Concept: As the beam is perpendicular to the central axis, all the y components of the force are cancelled out. So, the total force is due to the x components only. Using the pressure and the force relation of the electromagnetic wave, we can calculate the force per unit length. 2) Formula: i) d F x = 2 d F cos ⁡ θ ii) p r = 2 I cos 2 ⁡ θ C 3) Given: i) The intensity of the beam is I . ii) The radius of the totally reflecting cylinder is R . iii) The beam is perpendicular to the central axis of the cylinder. iv) The diameter of the beam is larger than 2 R . 4) Calculations: As the beam is perpendicular to the central axis, all the y components of the force are cancelled out. So, the total force is due to the x components only. The x component force equation can be written as d F x = 2 d F cos ⁡ θ where the force is pressure per unit area. Here, the pressure is radiation pressure. So, the radiation pressure is given by the equation as d F x = 2 ( p r d A ) cos ⁡ θ But the radiation pressure can be written as p r = 2 I cos 2 ⁡ θ C And the area element is d A = R L d θ So, the force per unit length can be calculated as F x = ∫ 2 2 I cos 2 ⁡ θ C cos ⁡ θ R L d θ F x L = ∫ 4 I cos 3 ⁡ θ C R d θ F x L = ∫ 0 π 2 4 I cos 2 ⁡ θ C R d θ F x L = 4 I R C ∫

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Question

Chapter 33, Problem 99P

To determine

To find:

The beam’s force per unit length on the cylinder.

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Chapter 33, Problem 98P

Chapter 33, Problem 100P

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