Explanation Given data : Consider that the power and diameter of the beam are 1 mW and 1 mm respectively. Explanation: Consider the following expression, which relates the electric and magnetic field amplitudes. E 0 = c B 0 (1) Here, c is the velocity of light in vacuum, which is generally 3 × 10 8 m s . Consider the following expression that relates the intensity of microwaves with oscillating electric field amplitude. I = c ε 0 E 0 2 2 (2) Here, ε 0 is permittivity of free space, which is generally known as 8.85 × 10 − 12 C 2 N ⋅ m 2 Re-arrange equation (2). E 0 2 = 2 I c ε 0 Take square root on both sides of the equation. E 0 = ( 2 I c ε 0 ) 1 2 (3) Consider the following expression that relates the intensity of microwaves with power and area of cross-section of the beam. I = P A (4) Here, A is cross-sectional area of the beam, which is generally π r 2 for circular beam. Substitute equation (4) in (3), E 0 = ( 2 P A c ε 0 ) 1 2 = ( 2 P A c ε 0 ) 1 2 Substitute π r 2 for A , E 0 = ( 2 P π r 2 c ε 0 ) 1 2 Here, r is the radius of the beam, which is equal to half value of diameter ( d ) of the beam. Therefore, d 2 = 1 mm 2 = 0.5 mm . Substitute 1 mW for P , 0.5 mm for r , 3 × 10 8 m s for c , and 8.85 × 10 − 12 C 2 N ⋅ m 2 for ε 0 in equation (3), E 0 = ( 2 ( 1 mW ) π ( 0.5 mm ) 2 ( 3 × 10 8 m s ) ( 8

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 25, Problem 29P

To determine

To find: The amplitudes of oscillating electric and magnetic fields in the laser beam.

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Chapter 25, Problem 28P

Chapter 25, Problem 30P

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