Subjects

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What is an Electromagnetic Wave? | 10 mins | 0 completed | Learn |

The Electromagnetic Spectrum | 10 mins | 0 completed | Learn |

Energy Carried by Electromagnetic Waves | 12 mins | 0 completed | Learn |

Electromagnetic Waves as Sinusoidal Waves | 7 mins | 0 completed | Learn |

Polarization Filters | 21 mins | 0 completed | Learn |

Displacement Current and Maxwell's Equations | 12 mins | 0 completed | Learn |

Concept #1: Electromagnetic Waves as Sinusoidal Waves

**Transcript**

Hey guys in this video we're going to talk about electromagnetic waves mathematically described as sinusoidal waves, let's get to it. Now as we know a common electromagnetic wave can be represented as a sinusoidal wave or sorry as an electric and magnetic field both of which are sinusoidal the image above me was the image that we saw before and this is the most common image for an electromagnetic wave we have in this case an electric field pointing in the X direction right we have an electrical in the X direction we have a magnetic field in the Y direction and we have propagation in the Z direction this makes our wave as we know a transverse wave because indeed the direction of propagation is perpendicular to both directions of oscillation. The direction of oscillation for the electric field and the direction of oscillation for the magnetic field so if we want to describe this mathematically we would write them as sine functions for example the electric field there would be some maximum electric field which is that amplitude of oscillation times sine of K X minus omega T. Omega we already know because we've seen this in oscillating functions before is the angular frequency of oscillation but K is something new it's called the wave number and I'll explain what it is and one second. Now to make this a vector we have the say in what direction the electric field is oscillating in our case it's oscillating in the X direction so I'll give it an I hat the magnetic field is going to be described the exact same way because if you look at the waves the oscillations in the above picture their identical except that the magnetic field is 90 degrees from the electric field so this is going to be some maximum magnetic field B max times sine of once again K, X minus omega T and I need to give it a direction and I'll say since its moving in the Y direction sorry since it's oscillating in the Y direction. These are Js by the way I made a little mistake here those X's are not X's those X's are Z's. That's the position along the propagation direction those are Z's since it's propagating in the Z direction alright now what the wave number is is it's related to the wave length it's just two Pi divided by the wave length and we know how to relate the angular frequency to things like the frequency and things like the period because we've done it many times before so let's do a quick example and get out here.

The following are the electric and magnetic fields let me leave equations, the following are the electric and magnetic fields that describe a particular electromagnetic wave what is the wavelength of this wave? What is the period? I'm going to address the period first just because what I am most comfortable with but it really doesn't matter how you do them because one answer does not depend upon the other this is the angular frequency in both cases. That's the quantity that we know is related to the wavelength sorry to the period we know that the angular frequency is 2 Pi over the period so we know that this is going to be 2 Pi over 4.19 times 10 to the 15 and so wops sorry I forgot a step there and so if I want to isolate the period I got to multiply the period up and divided the wavelength over so the period is 2 Pi over the wave length which is going to be 2 Pi over 4.19 times 10 to the 15 right that's the angular frequency and this whole thing is going to equal 1.5 times 10 to the -15 seconds which is an incredibly small number because the frequency is an incredibly large number we would expect the period to be very very very small if the frequency is very very very high now we want to address the wave number. We have our equation in red above in the green box for what the wave number is and we know that these numbers are both the wave numbers and the wave number is related to our wave length which is what we want to find so I can multiply the wavelength up and I can divide that over and I can get to the wavelength is 2 Pi over K. Which is 2 Pi over 1.4 times 10 to the 7. Which is going to be 450 or so times 10 to the -9 meters. I've chosen to write it like this for a particular reason because this can then be written as 450 nanometers which is blue light. So those are our two answers, now these two numbers have to actually be related to one another for multitude of reasons first of all we know that lambda divided by the period has to be the speed of the wave which is in this case light and you'll see that if you do take lambda and you do take the period and you divide them you will get C. That's one way to confirm that this is in fact a correct wave another way is to just take omega and divide it by K. Both of which are already represented in this equation, in the functions that will also equal the speed of light and finally we know that the ratio of E max to B max has to be the speed of light and if I wrote these functions correctly I check the multiple times I'm pretty sure I did all three of these relationships should be true. Alright guys that wraps up our discussion on electromagnetic waves as sinusoidal waves. Thanks for watching.

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Concept #1: Electromagnetic Waves as Sinusoidal Waves

At an instant of time and at a particular location in space, the electric field of an electromagnetic wave is in the -x-direction and the magnetic field is in the +y-direction. What is the direction in which the wave is traveling?
A) +x
B) -x
C) +y
D) -y
E) +z
F) -z

An electromagnetic wave propagates through a vacuum in the +x-direction, carrying an intensity of 150 W/m2. At t = 0, the electric field has zero amplitude, and after 0.01 s, the electric field strength grows to its maximum value, pointing in the +y direction. Write equations describing the electric and magnetic fields as sinusoidal oscillations, including the appropriate unit vectors to denote direction.

At a certain instant in time, an electromagnetic wave has Ē in the +z direction and B in the +y direction. In what direction does the wave propagate?A) -x directionB) +x directionC) +y directionD) -z directionE) +z direction

The y component of the electric field of an electromagnetic wave travelling in the +x direction through vacuum obeys the equation Ey = (375 N/C) cos [kx − (2.20 × 10 14 rad/s)t]. What is the wavelength of this electromagnetic wave?
a. 0.272 μm
b. 1.36 μm
c. 2.72 μm
d. 8.57 μm
e. 17.1 μm

The magnetic field of a plane EM wave is given by: B = (E0/c) sin(kz + ωt) i The electric field of the wave would be given by:A. E = +E0 sin(kz + ωt) jB. E = +E0 cos(kz + ωt) kC. E = +E0 cos(kz + ωt) jD. E = –E0 cos(kz + ωt) iE. E = –E0 cos(kz + ωt) i

A sinusoidal electromagnetic wave propogates in the -y direction in a medium with a refractive index of 1.5, with a magnetic field amplitude of 0.001 T and a wavelength of 1.55 nm.
(a) What is the angular frequency of the wave?
(b) What is the electric field amplitude of the wave?
(c) What is the intensity of the wave?

At one instant the electric and magnetic fields at one point of an electromagnetic wave are E = (25 î + 350 ĵ - 50 k̂) V/m and B = B0 (7.2 î - 7.0 ĵ + a k̂) μTWhat is the value of a?

The magnetic field of an electromagnetic wave in a vacuum is Bz = (2.4 µT)sin((1.14×107)x - ? t), where x is in m and t is in s.(a) What is the wave's wavelength?(b) What is the wave's frequency?(c) What is the wave's electric field amplitude?

A. For a sine function with amplitude A=0.75 and period T=10, what is y(4)?B. For a cosine function with amplitude A=0.75 and period T=10, what is y(4)?

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction.Part AIf at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.40V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time?Part BWhat is the direction of the magnetic field?

The microwaves in a certain microwave oven have a wavelength of 12.2 cm.Part A. How wide must this oven be so that it will contain five antinodal planes of the electric field along its width in the standing wave pattern?L = cmPart B. What is the frequency of these microwaves?f = HzPart C. Suppose a manufacturing error occurred and the oven was made 6.0cm longer than specified in part (a). In this case, what would have to be the frequency of the microwaves for there still to be five antinodal planes of the electric field along the width of the oven?f = Hz

The magnetic field of an electromagnetic wave in a vacuum is Bz =(4.0μT)sin((1.20×107)x−ωt), where x is in m and t is in s.a. What is the wave's wavelength?b. What is the wave's frequency?c. What is the wave's electric field amplitude?

1) Which equation correctly describes the electromagnetic wave shown above? Briefly explain your reasoning.a) Ex = Eo sin(kz + wt)b) Ey = Eo sin(kz - at)c) By = Bo sin(kz - wt) 2) Which of the following actions will increase the energy carried by this wave? Briefly explain your reasoning.a) Increase E keeping w constantb) Increase w keeping E constantc) Both of the above actions will increase the energy of the waved) Neither of the above actions will increase the energy of the wave.

,.This wave is linearly polarized in the y-direction. a. What is the wavelength λ of the wave described in the problem introduction?b. What is the period T of the wave described in the problem introduction?c. What is the velocity v of the wave described in the problem introduction?

The fields of an electromagnetic wave are E→=Epsinkz+ωtj^ and B→=Bpsinkz+ωti^ Give a unit vector n^ in the direction of propagation.Express your answer in terms of the variablesi^,j^, andk^."

A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 μT and a wavelength of 432 nm is traveling in the +-direction through empty space.What is the frequency of this wave?

A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 μT and a wavelength of 432 nm is traveling in the +-direction through empty space.What is the amplitude of the associated electric field?

Dielectric breakdown in air occurs when the electric field is approximately 3 × 106 V/m.What would be the peak magnetic field in an electromagnetic wave with this value for its peak electric field?

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.40V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time?

A radio wave is traveling in the negative y-direction. What is the direction of E at a point where B is in the positive x-direction? A. −x-direction B. −y-direction C. +z-direction D. +y-direction E. +x-direction F. −z-direction

Consider each of the electric- and magnetic-field orientationsWhat is the direction of propagation of the wave if E = E î, B = - B ĵ. Express the direction of the propagation vector, P, as a unit vector. Its three components should be entered in order (x,y,z) separated by commas. For example, if the wave propagates only in the -x direction, enter -1,0,0. <-- for all of them

Consider each of the electric- and magnetic-field orientationsWhat is the direction of propagation of the wave if E = E î , B = - B k̂ . Express the direction of the propagation vector, P, as a unit vector. Its three components should be entered in order (x,y,z) separated by commas. For example, if the wave propagates only in the -x direction, enter -1,0,0. <-- for all of them

Consider each of the electric- and magnetic-field orientationsWhat is the direction of propagation of the wave if E = E ĵ , B = B î. Express the direction of the propagation vector, P, as a unit vector. Its three components should be entered in order (x,y,z) separated by commas. For example, if the wave propagates only in the -x direction, enter -1,0,0. <-- for all of them

Consider each of the electric- and magnetic-field orientationsWhat is the direction of propagation of the wave if E = - Ek^, B = - Bi^. Express the direction of the propagation vector, P, as a unit vector. Its three components should be entered in order (x,y,z) separated by commas. For example, if the wave propagates only in the -x direction, enter -1,0,0. <-- for all of them

To understand the formula representing a traveling electromagnetic wave. Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other. The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given byThis wave is linearly polarized in the y direction.What is the wavelength λ of the wave described in the problem introduction?

A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 μT and a wavelength of 432 nm is traveling in the +-direction through empty space.Write the equations for the electric and magnetic fields as functions of x and t in the form of Eqs. (32.17).

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