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The derivation for the speed of electromagnetic waves comes out of Maxwell\'s eq

ID: 1387716 • Letter: T

Question

The derivation for the speed of electromagnetic waves comes out of Maxwell's equations for electromagnetism. For this reason, the speed of an electromagnetic wave depends on electromagnetic constants. v = 1 / . (Note: the speed of an electromagnetic wave in vacuum is given the variable c. Some books highlight the equation c = 1 / , which is just a special case of this general equation in vacuum.) In a vacuum, epsilon = epsilon 0 = 8.85 Times 10-12 C2 / Nm2 and mu = mu 0 = 4 pi Times 10-7Tm / A. Calculate the speed of an electromagnetic wave in vacuum. In water, an electromagnetic wave has frequency 5 Times 1015 Hz and wavelength 45 nm . By what factor is the speed of this electromagnetic wave slower than the speed of an electromagnetic wave in vacuum? In glass, an electromagnetic wave has frequency 5 Times 1015 Hz and wavelength 40 nm . By what factor is the speed of this electromagnetic wave slower than the speed of an electromagnetic wave in vacuum?

Explanation / Answer

a)

v=sqrt(1/mu*epsilon)

=sqrt(1/4*3.14*10-7*8.85*10-12)

=sqrt(8.99*1016)

=3*108m/s

b)

speed of electromagneticwave in water=5*1015*45*10-9

=225*106m/s

speed of electromagneticwave in vaccum=3*108/225*106 speed of electromagneticwave in vaccum

=1.33speed of electromagneticwave in vaccum

c)

speed of electromagneticwave in water=5*1015*40*10-9

=200*106m/s

speed of electromagneticwave in vaccum=3*108/200*106 speed of electromagneticwave in vaccum

=1.5speed of electromagneticwave in vaccum