4. We have a plane wave in vacuum with direction of propagation along the wave vector k (real vector) and angular frequency w. Ē, is a (possibly) complex, but constant vector. Then, the electric field vector is (time t and position vector ř ): Ē(F,t)=Re{E, expli(k.F – wt)} Derive the following properties of a plane wave using Maxwell's equations and the material equations. a) Write the Maxwell's equation in the vacuum. (b)Derive the wave equation and show that E(F,t) is the solution of the wave equation (c) Which condition has to be valid for the vectors k and Ē relatively to each other? Use one of Maxwell's equations for deriving this condition. d) Calculate the magnetic induction B in dependence on the electric field vector and especially the ratio of the moduli of both quantities. e) State the Poynting theorem (f) Calculate the Poynting vector (time-dependent and time-independent) in dependence on the electric field vector and give the physical meaning of the pointing yector

4. We have a plane wave in vacuum with direction of propagation along the wave vector k (real vector) and angular frequency w. Ē, is a (possibly) complex, but constant vector. Then, the electric field vector is (time t and position vector ř ): Ē(F,t)=Re{E, expli(k.F – wt)} Derive the following properties of a plane wave using Maxwell's equations and the material equations. a) Write the Maxwell's equation in the vacuum. (b)Derive the wave equation and show that E(F,t) is the solution of the wave equation (c) Which condition has to be valid for the vectors k and Ē relatively to each other? Use one of Maxwell's equations for deriving this condition. d) Calculate the magnetic induction B in dependence on the electric field vector and especially the ratio of the moduli of both quantities. e) State the Poynting theorem (f) Calculate the Poynting vector (time-dependent and time-independent) in dependence on the electric field vector and give the physical meaning of the pointing yector

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

please answer this question
Can you help me with this problem? (See attached image)
Consider a 10 cm tall object placed 60 cm from a concave mirror with a focal length of 40 cm. The size of the image is
You measure an object distance of 0.3 m and an image distance of 0.15. Will the image be larger or smaller than the original object?
An object is placed 60 cm in front of a concave mirror with a focal length of 12 cm. Where is the image located?
please check image
An image formed by a concave mirror is mostly (except for cases when the object is placed too closed to the mirror) real and inverted real and straight / erect virtual and straight virtual and inverted
An object 24.0 cm from a concave mirror creates a virtual image at -33.5 cm. If the image is 7.25 cm tall, what is the height of the object? (Mind your minus signs.) (Unit = cm)
Calculate the image distance when an object is placed 6 cm in front of a mirror with focal length -10 cm.(Give your answer in centimeters but don't include units in your answer.)
For a spherical mirror, if the object distance is 24.2cm and the focal length is -8.7cm, find the image distance in units of cm. (Give your answer with 1 decimal and do not forget to express the sign of your answer)
F= 30 cm 40 cm 60 cm Where is the position of final image and its properties? Final answer : 200 cm in front of mirror and final image is real and erect
An object with height of 2.5 cm is placed a distance of 25.5 cm from a convex mirror having a focal length of -12.2 cm. Determine the image distance and the image height.