Several Questions About Electromagnetic Waves

[jaketodd]

In what direction does the magnetic component of an EM wave oscillate?

Is there a lateral end to the interference pattern created in the double slit experiment, and if so, what defines it?

How fast do EM waves expand laterally?

In the double slit experiment, what makes the interference pattern's bright stripes get smaller and dimmer as you look laterally at the pattern? Is it due to amplitude lessening with distance? If so, how is it we can see starlight? Can we see starlight because the frequency doesn't lessen with distance and the frequency determines how much energy is transferred to our eyes? If so, why can we look at stars and our eyes don't hurt but looking at the sun does hurt our eyes?

If you aim the emitter in the double slit experiment at an angle to the two slits, does the interference pattern shift as well?

How curved is the wavefront of an EM wave; is it a semicircle?

Are the amplitudes of the electric and magnetic oscillations the same? How does one calculate the amplitude of each?

Thanks!

Jake

 

[pellman]

I am going to answer these from a classical point of view.

In what direction does the magnetic component of an EM wave oscillate?

Both electrical and magnetic components oscillate perpendicular to the direction of motion, and perpendicular to each other.

Is there a lateral end to the interference pattern created in the double slit experiment, and if so, what defines it?

How fast do EM waves expand laterally?

don't know what you mean by laterally here.

In the double slit experiment, what makes the interference pattern's bright stripes get smaller and dimmer as you look laterally at the pattern? Is it due to amplitude lessening with distance?

Yes. The luminosity of a light source falls off as 1/r^2.

If so, how is it we can see starlight? Can we see starlight because the frequency doesn't lessen with distance and the frequency determines how much energy is transferred to our eyes?

Even though the distance is so great, the source luminosity is great enough that at this distance the luminosity is still within the range of detection by the human eye. Frequency only has to do with the range of light that is visible (at any brightness).

If so, why can we look at stars and our eyes don't hurt but looking at the sun does hurt our eyes?

The difference is the intensity. the greater the distance, the less intense. (The amount of energy transferred is proportional to the intensity-squared, and the greater the energy, the more potential damage done to the eye)

If you aim the emitter in the double slit experiment at an angle to the two slits, does the interference pattern shift as well?

yes

How curved is the wavefront of an EM wave; is it a semicircle?

This depends on the source. But the further away from the source you get, the more approximately spherical it will be.

Are the amplitudes of the electric and magnetic oscillations the same?

Depends on what units you work in. In Gaussian units, electrical and magentic fields have the same units and the same amplitudes.

How does one calculate the amplitude of each?

calculating the amplitudes would require you to know what the source is. It's rather complicated. See for instance the chapters on radiation in Jackson's Electromagnetic Theory.

 

[jtbell]

For the E and B fields produced by a "Hertzian dipole," at distances "far" from the source, see for example

http://farside.ph.utexas.edu/teaching/em/lectures/node94.html

in particular equations 1090 and 1091. At "near" distances, things get more complicated.

 

[jaketodd]

don't know what you mean by laterally here.

By laterally, I mean: Is there an end to the interference pattern on the screen behind the two slits as you look further and further to the sides of the screen and getting further from the two slits. I'm talking about as you look farther and farther, for instance to the left on the screen, I know the interference pattern gets dimmer but does it ever end?

Thanks,

Jake

 

[jaketodd]

Both electrical and magnetic components oscillate perpendicular to the direction of motion, and perpendicular to each other.

How can something be perpendicular to something that is perpendicular to something else and be perpendicular to that something else at the same time? I can't visualize this. Please help.

Does the magnetic field oscillate at all towards the direction of propagation? In other words, does the magnetic field oscillate in front or behind the wavefront at all?

I'm assuming that the wavefront is a curve with the electric field oscillating up and down and the peaks and valleys spread across the curve, so if you were looking at the wavefront coming toward you, you'd see an oscillating sine wave pattern. Is this correct?

I watched this video:
Is it true that's the direction of propagation of an EM wave? I thought the wavefront moving forward was curved with many valleys and peaks oscillating across it. I am confused :-S

If that's how EM waves propagate, how is the double slit experiment explained? I thought the wavefronts from the two waves emerging from the slits expanded and interfered with each other. How could that happen if they propagate like that video shows?

Thanks,

Jake

 

[pellman]

I know the interference pattern gets dimmer but does it ever end?

Classical wave theory would say it never ends but gets infinitesimally dim. But at that point we can no longer approximate it with classical theory and need to go quantum. There is a point at which the interference pattern would seem to actually disappear because you only get the occasional lone photon hitting the screen. However... if you made observation for a long enough time--years maybe--and kept track of all the photons that hit the screen, no matter how far you go out on the screen eventually the sum of all the photons hitting the screen would show the interference pattern.

How can something be perpendicular to something that is perpendicular to something else and be perpendicular to that something else at the same time?

Look at a corner of your room. Two walls perpendicular to each other meet and both are perpendicular to the floor.

Does the magnetic field oscillate at all towards the direction of propagation? In other words, does the magnetic field oscillate in front or behind the wavefront at all?

Not in free space. Though, if I remember correctly, inside a wave guide (like a co-axial cable or fiber optic cable) it can do this.

I'm assuming that the wavefront is a curve with the electric field oscillating up and down and the peaks and valleys spread across the curve, so if you were looking at the wavefront coming toward you, you'd see an oscillating sine wave pattern. Is this correct?

yes

I watched this video:
Is it true that's the direction of propagation of an EM wave? I thought the wavefront moving forward was curved with many valleys and peaks oscillating across it. I am confused :-S

The animation is showing what happens at a single observation point. However, what we usually mean by a wave-front is a curve of constant amplitude. As you move along the wave (laterally) you have the same value (whether peak or trough) at any given time. Think of a string of water waves coming in parallel to a shore which is aligned north-south. At any fixed time as you move north or south along the waves at some fixed distance from shore, the height of water is constant. It is only along a line not aligned with the waves that would cut across the peaks and troughs.

If that's how EM waves propagate, how is the double slit experiment explained? I thought the wavefronts from the two waves emerging from the slits expanded and interfered with each other. How could that happen if they propagate like that video shows?

Picture the same animation but with two waves coming in from different directions and converging on the observation point. The sum of the two is what is observed. If they have the same phase, they add constructively and the result is "twice as bright". If their relative phases are such that they are always opposite--one is down when the other is up and vice versa--the destructively interfere and you get a dark spot.

 

[jaketodd]

Ok, first of all, thank you for bearing with me. I have a question:

You said "yes" to me asking "I'm assuming that the wavefront is a curve with the electric field oscillating up and down and the peaks and valleys spread across the curve, so if you were looking at the wavefront coming toward you, you'd see an oscillating sine wave pattern. Is this correct?"

So if we picture that same image, with the electric field oscillating up and down, would the magnetic oscillations be moving from side to side, seen to you as crests and valleys, but lateral crests and valleys (remember the wavefront is coming at you)? If not, what would they look like?

Thanks,

Jake

 

[ZapperZ]

How can something be perpendicular to something that is perpendicular to something else and be perpendicular to that something else at the same time? I can't visualize this. Please help.

Draw a standard 3D cartesian coordinate. The x, y, and z axis are all perpendicular to each other. This is no different than the E, B, and the propagation direction of light.

Zz.

 

[pellman]

So if we picture that same image, with the electric field oscillating up and down, would the magnetic oscillations be moving from side to side?

Correct.

It follows from the two maxwell equations which in the absence of electrical charges read

$$\nabla\times \vec{B}=\frac{1}{c}\frac{\partial\vec{E}}{\partial t}$$
$$\nabla\times \vec{E}=-\frac{1}{c}\frac{\partial\vec{B}}{\partial t}$$

$$\nabla\times$$ is the "curl" operation, the result of which is perpendicular to the vector it acts on. On the right hand side we have time-derivatives which mean "rate of change".

So it means a changing E-field produces a B-field at right angles to the change and vice versa. The undulating E-field produces a B-field, and the undulating B-field in turn produces an E-field, and so on, and so on.

The c in the equations give the speed of the wave: the speed of light.

 

[jaketodd]

Correct.

It follows from the two maxwell equations which in the absence of electrical charges read

$$\nabla\times \vec{B}=\frac{1}{c}\frac{\partial\vec{E}}{\partial t}$$
$$\nabla\times \vec{E}=-\frac{1}{c}\frac{\partial\vec{B}}{\partial t}$$

$$\nabla\times$$ is the "curl" operation, the result of which is perpendicular to the vector it acts on. On the right hand side we have time-derivatives which mean "rate of change".

So it means a changing E-field produces a B-field at right angles to the change and vice versa. The undulating E-field produces a B-field, and the undulating B-field in turn produces an E-field, and so on, and so on.

The c in the equations give the speed of the wave: the speed of light.

So just to make sure, (imagining you could see the oscillations) if the wavefront is coming directly at you (the EM wave is emitted directly at you), you would actually see the peaks and valleys of the magnetic oscillations? You would see the curvature of their peaks and valleys oscillating right and left?

Thank you for your patience,

Jake

 

[jaketodd]

(continuing from my last post (please read it first))...and you would see the curvature of the electric peaks and valleys oscillating up and down?

So, in the attached picture of an EM wave coming at you, the black would be the electric oscillations and the blue would be the magnetic oscillations?

Thanks!

Jake

 

[Born2bwire]

You don't really "see" anything (let's ignore our physical sensation of light). Electromagnetic waves describe a force on a given charge quantity. So if you were to place a test charge at your point of observation, the electromagnetic wave equations would tell you what force in time that the test charge will experience. So if we keep our test charge at a constant point in space, it will experience an oscillating force. The first order from the electric field and a second order force from the magnetic field (which would arise if we let our test charge move).

In regards to ZapperZ's (pew pew!) comments, the electric and magnetic field vectors are situated in three dimensional space and are mutually orthogonal to each other and, in most cases but not all, to the direction of the wave's propagation. For example, if the wave is propagating along the z-axis, then the electric field vector can point along the x-axis and the magnetic field vector along the y-axis. In this manner all three vectors (electric, magnetic, propagation) are mutually orthogonal.

 

[jaketodd]

But pellman said "Not in free space" to my question of "Does the magnetic field oscillate at all towards the direction of propagation? In other words, does the magnetic field oscillate in front or behind the wavefront at all?"

Wouldn't that necessitate the magnetic component oscillating as in the picture attached to my last post? Isn't that what it would be like for a single EM wave coming directly at you?

 

[jaketodd]

And he said "yes" to me asking "I'm assuming that the wavefront is a curve with the electric field oscillating up and down and the peaks and valleys spread across the curve, so if you were looking at the wavefront coming toward you, you'd see an oscillating sine wave pattern. Is this correct?"

So wouldn't it look like that image I attached?