Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

Question
Book Icon
Chapter 34, Problem 16P
To determine

The verification for E=Emaxcos(kxωt) and B=Bmaxcos(kxωt) being the solution to equations 34.15 and 34.16 respectively.

Expert Solution & Answer
Check Mark

Answer to Problem 16P

The verification for E=Emaxcos(kxωt) and B=Bmaxcos(kxωt) being the solution to equations 34.15 and 34.16 respectively is as stated below.

Explanation of Solution

The given equations are.

    E=Emaxcos(kxωt)                                                                                                 (I)

Here, E is the magnitude of electric field , Emax is the magnitude of the maximum electric field, k is the wave vector and ω is the angular frequency.

    B=Bmaxcos(kxωt)                                                                                               (II)

Here, B is the magnitude of magnetic field , Bmax is the magnitude of the maximum magnetic field.

Differentiate equation (I) partially twice with respect to x.

    Ex=Emaxsin(kxωt)(k)2Ex2=Emaxcos(kxωt)(k2)                                                                                (III)

Differentiate equation (I) partially twice with respect to t.

    Et=Emaxsin(kxωt)(ω)2Et2=Emaxcos(kxωt)(ω)2                                                                               (IV)

Differentiate equation (II) partially twice with respect to x.

    Bx=Bmaxsin(kxωt)(k)2Bx2=Bmaxcos(kxωt)(k2)                                                                                 (V)

Differentiate equation (II) partially twice with respect to t.

    Bt=Bmaxsin(kxωt)(ω)2Bt2=Bmaxcos(kxωt)(ω)2                                                                               (VI)

Divide equation (III) by equation (IV).

    2Ex22Et2=Emaxcos(kxωt)(k2)Emaxcos(kxωt)(ω)22Ex2=k2ω2(2Et2)                                                                          (VII)

Divide equation (V) by equation (VI).

    2Bx22Bt2=Bmaxcos(kxωt)(k2)Bmaxcos(kxωt)(ω)22Ex2=k2ω2(2Bt2)                                                                         (VIII)

Also,

    kω=μ0ε0                                                                                                              (IX)

Here, μ0 is the permeability of the medium and ε0 is the permittivity if the medium.

Substitute μ0ε0 for kω in equation (VII).

    2Ex2=(μ0ε0)2(2Et2)2Ex2=μ0ε0(2Et2)                                                                                           (X)

The equation 34.15 is ,

    2Ex2=μ0ε0(2Et2)                                                                                                 (XI)

Substitute μ0ε0 for kω in equation (VIII).

    2Bx2=(μ0ε0)2(2Bt2)2Bx2=μ0ε0(2Bt2)                                                                                          (XII)

The equation 34.16 is,

    2Bx2=μ0ε0(2Bt2)                                                                                              (XIII)

Conclusion:

Equation (X) is equal to equation (XI) and equation (XII) equals to equal (XIII).

Hence, verified.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
ROTATIONAL DYNAMICS Question 01 A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure rolling motion Question 02 A sphere and cylinder of the same mass and radius start from ret at the same point and more down the same plane inclined at 30° to the horizontal Which body gets the bottom first and what is its acceleration b) What angle of inclination of the plane is needed to give the slower body the same acceleration Question 03 i) Define the angular velocity of a rotating body and give its SI unit A car wheel has its angular velocity changing from 2rads to 30 rads seconds. If the radius of the wheel is 400mm. calculate ii) The angular acceleration iii) The tangential linear acceleration of a point on the rim of the wheel Question 04 in 20
Question B3 Consider the following FLRW spacetime: t2 ds² = -dt² + (dx² + dy²+ dz²), t2 where t is a constant. a) State whether this universe is spatially open, closed or flat. [2 marks] b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. [3 marks] c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A. d) The Friedmann equations are 2 k 8πG а 4πG + a² (p+3p). 3 a 3 [5 marks] Use these equations to determine the energy density p(t) and the pressure p(t) for the FLRW spacetime specified at the top of the page. [5 marks] e) Given the result of question B3.d, state whether the FLRW universe in question is (i) radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv) none of the previous. Justify your answer. f) [5 marks] A conformally…
SECTION B Answer ONLY TWO questions in Section B [Expect to use one single-sided A4 page for each Section-B sub question.] Question B1 Consider the line element where w is a constant. ds²=-dt²+e2wt dx², a) Determine the components of the metric and of the inverse metric. [2 marks] b) Determine the Christoffel symbols. [See the Appendix of this document.] [10 marks] c) Write down the geodesic equations. [5 marks] d) Show that e2wt it is a constant of geodesic motion. [4 marks] e) Solve the geodesic equations for null geodesics. [4 marks]

Chapter 34 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

Ch. 34 - Prob. 4OQCh. 34 - Prob. 5OQCh. 34 - Prob. 6OQCh. 34 - Prob. 7OQCh. 34 - Prob. 8OQCh. 34 - Prob. 9OQCh. 34 - Prob. 10OQCh. 34 - Prob. 11OQCh. 34 - Prob. 1CQCh. 34 - Prob. 2CQCh. 34 - Prob. 3CQCh. 34 - Prob. 4CQCh. 34 - Prob. 5CQCh. 34 - Prob. 6CQCh. 34 - Prob. 7CQCh. 34 - Do Maxwells equations allow for the existence of...Ch. 34 - Prob. 9CQCh. 34 - Prob. 10CQCh. 34 - Prob. 11CQCh. 34 - Prob. 12CQCh. 34 - Prob. 13CQCh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4PCh. 34 - Prob. 5PCh. 34 - Prob. 6PCh. 34 - Prob. 7PCh. 34 - Prob. 8PCh. 34 - The distance to the North Star, Polaris, is...Ch. 34 - Prob. 10PCh. 34 - Prob. 11PCh. 34 - Prob. 12PCh. 34 - Prob. 13PCh. 34 - Prob. 14PCh. 34 - Prob. 15PCh. 34 - Prob. 16PCh. 34 - Prob. 17PCh. 34 - Prob. 18PCh. 34 - Prob. 19PCh. 34 - Prob. 20PCh. 34 - If the intensity of sunlight at the Earths surface...Ch. 34 - Prob. 22PCh. 34 - Prob. 23PCh. 34 - Prob. 24PCh. 34 - Prob. 25PCh. 34 - Review. Model the electromagnetic wave in a...Ch. 34 - Prob. 27PCh. 34 - Prob. 28PCh. 34 - Prob. 29PCh. 34 - Prob. 30PCh. 34 - Prob. 31PCh. 34 - Prob. 32PCh. 34 - Prob. 33PCh. 34 - Prob. 34PCh. 34 - Prob. 35PCh. 34 - Prob. 36PCh. 34 - Prob. 37PCh. 34 - Prob. 38PCh. 34 - Prob. 39PCh. 34 - The intensity of sunlight at the Earths distance...Ch. 34 - Prob. 41PCh. 34 - Prob. 42PCh. 34 - Prob. 43PCh. 34 - Extremely low-frequency (ELF) waves that can...Ch. 34 - Prob. 45PCh. 34 - A large, flat sheet carries a uniformly...Ch. 34 - Prob. 47PCh. 34 - Prob. 48PCh. 34 - Prob. 49PCh. 34 - Prob. 50PCh. 34 - Prob. 51PCh. 34 - Prob. 52PCh. 34 - Prob. 53PCh. 34 - Prob. 54APCh. 34 - Prob. 55APCh. 34 - Prob. 56APCh. 34 - Prob. 57APCh. 34 - Prob. 58APCh. 34 - One goal of the Russian space program is to...Ch. 34 - Prob. 60APCh. 34 - Prob. 61APCh. 34 - Prob. 62APCh. 34 - Prob. 63APCh. 34 - Prob. 64APCh. 34 - Prob. 65APCh. 34 - Prob. 66APCh. 34 - Prob. 67APCh. 34 - Prob. 68APCh. 34 - Prob. 69APCh. 34 - Prob. 70APCh. 34 - Prob. 71APCh. 34 - Prob. 72APCh. 34 - Prob. 73APCh. 34 - Prob. 74APCh. 34 - Prob. 75APCh. 34 - Prob. 76CPCh. 34 - Prob. 77CPCh. 34 - Prob. 78CPCh. 34 - Prob. 79CP
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
University Physics Volume 2
Physics
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning