Consider an electromagnetic wave traveling in vacuum. Recall that the speed of l
ID: 1379209 • Letter: C
Question
Consider an electromagnetic wave traveling in vacuum. Recall that the speed of light in vacuum is c = 3 x 10^8 m/s. The electric field corresponding to this wave is given by: Vector E = (10 V/m) cos(ky + 2 pi . 10^12s ^-1 t)i hat + (10 V/m) cos(ky + 2 pi . 10^12s^-1.t)k hat (1) Here hat i, j, and k are perpendicular unit vectors associated with the cartesian coordinates x, y, and z respectively. (a) What is the direction of propagation of this wave? (b) What is the frequency f in Hertz and the wavelength A in meters? (c) What is the corresponding magnetic field? (d) A totally absorbing detector of area A = 10 cm^2 lies perpendicularly to the direction of propagation. How much energy is absorbed by the detector in one second?Explanation / Answer
a) Direction of propogation of wave is along y - axis.
b)
Frequency
f = w / 2 pi = 2pi 10^ 12 / 2 pi = 10 ^ 12 Hz
wavelenght
lamda = v / f = 3*10^ 8 m/s / 10 ^ 12 = 0.0003 m
c)
magnetic field B = E / c = (10 V/ m ) / 3 * 10 ^ 8 m/s = 3.33*10^ -8 T
d)
energy / sec = intensity x area
= ( 1/2) e_o c E^2 x area
= (0.5 ) ( 8.85*10^ -12 ) ( 3 *10^ 8 ) ( 10 V / m ) ^2 (10 *10^ -4 m ^2 )
= 1.32*10^ -4 J /s