1 2 3 4 5 6 7 8 The magnetic field in a plane monochromatic electromagnetic wave
ID: 1796555 • Letter: 1
Question
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The magnetic field in a plane monochromatic electromagnetic wave with wavelength = 583 nm, propagating in a vacuum in the z-direction is described by
B =(B1sin(kzt))(i^+j^)B=(B1sin(kzt))(i^+j^)
where B1 = 7.9 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.
1)
What is k, the wavenumber of this wave?
m-1
2)
What is zmax, the distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t = 0?
nm
3)
What is Emax, the amplitude of the electric field oscillations?
V/m
4)
What is Ey, the y-component of the electric field at (x = 0, y-0, z = zmax) at t = 0?
V/m
5)
Which of the following equations describes the spatial and time dependence of the electric field oscillations?
6)
What is tmax, the first time after t = 0, when the magnitude of the electric field at the origin (x = y = z = 0) has its maxiumum value?
s
- in - 07+)Explanation / Answer
1) k = 2*pi/lamda
= 2*pi/(583*10^-9)
= 1.08*10^7 rad/m
2) B = Bmax*sin(k*z - w*0)
when B = Bmax, sin(k*z) = 1
when k*z = pi/2
z = (pi/2)*k
= (pi/2)/(1.08*10^7)
= 1.45*10^-7 m
3) Emax = Bmax*c
= 7.9*10^-6*3*10^8
= 2370 V/m
4) E = Emax/sqrt(2)
= 2370/sqrt(2)
= 1676 V/m
5) 3rd option is the correct answer.
6) t = T
= 1/f
= 1/(c/lamda)
= lamda/c
= 583*10^-9/(3*10^8)
= 1.94*10^-15 s
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