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Verbatim question for GR8677 #3
Electromagnetism}Wave Equation

Simply and elegantly stated: \frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2}=\frac{\partial^2 \phi}{\partial x^2}. (One can check this by noting that the dimensions cancel out to meters^{-2} on both sides.) Now, c=\frac{1}{\sqrt{\epsilon_0 \mu_0}}. Elsewhere than a vacuum, it's v=\frac{1}{\sqrt{\epsilon \mu}}, where, in this problem, we have \epsilon=2.1\epsilon_0 and \mu=\mu_0.
\par
No need to narrow the choices down. (D) is right because v=\frac{1}{\sqrt{2.1 \times 1 \epsilon_0 \mu_0}}=\frac{c}{\sqrt{2.1}}, where the last equality comes from substituting the definition of the speed of light (via an epsilon and a mu).

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Comments
rehab
2009-10-27 18:13:50
the answer must be (B )otherwise groub velocity will exceed the speed of light from this realtion vp=c^2/vg and that ,of course, impossible!!rnNEC
smokwzbroiplytowej
2008-10-22 19:18:33
Not _exactly_ related to this problem, but Wikipedia has a nice applet showing the difference between group and phase velocity:

http://en.wikipedia.org/wiki/Group_velocity

Albert
2009-10-31 02:46:00
Yo all, that link ain't no good no more!

Check out this hot baby:

http://en.wikipedia.org/wiki/Wave#Phase_velocity_and_group_velocity



NEC
blue_down_quark
2008-08-02 09:10:29
I think the answer is incorrect. The question doesn't ask 'what is light's velocity ?' it instead asks 'what is light's PHASE VELOCITY? '. Phase velocity can actually be larger than c . The equation for phase velocity is v_pv_g = c^2 . I think the correct answer is B . for more information see : http://en.wikipedia.org/wiki/Phase_velocity
wangjj0120
2008-08-20 20:59:02
but when is the equation v_pv_g = c^2 valid?
To integrate this equation, we realize that
only when the light propagate in the air and wave guide (or plasma) have the dispersion relation which corresponds to this equation.
zaijings
2009-04-03 08:22:28
I am also confused when the problem asks about the phase velocity.
segfault
2009-08-22 21:06:49
I think when dealing with a signal of a single frequency (e.g., blue light), it only makes sense to talk about the phase velocity--you can't construct a "group" or wavepacket out of a single frequency signal.
jchys
2010-02-02 20:38:17
If you look at the section carefully, it says that
"any particle that has MASS (according to special relativity) phase velocity of matter waves always exceeds c"

photons obviously has no mass.
NEC
erc
2005-11-04 09:11:07
I don\'t know anything about this, so maybe about to make a fool of myself...

But, to be consistent, I think the and should each lose the power?

Thanks.
yosun
2005-11-04 15:10:14
erc: thanks for the typo note. The extra squared sign on the c's and v's have been removed. (you can also check it by dimensional analysis. the units for permeability and permittivity are given on the table of info included with the exam)
Fixed Typos!
erc
2005-11-04 09:09:06
rehab
2009-10-27 18:30:09
the answer must be (B )otherwise groub velocity will exceed the speed of light from this realtion vp=c^2/vg and that ,of cource, impossible!!

NEC

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