GREPhysics.NET: GR8677 #3

GR8677 #3

Problem

GREPhysics.NET Official Solution

Electromagnetism $\Rightarrow$ }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

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

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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 $v_p$ $v_g$ = $c^2$ . 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.

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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 $c^2$ and $v^2$ 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)

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erc
2005-11-04 09:09:06

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