Question

An EM wave has a wavelength A 500 nm and a peak electric field Eo 100 i. The wave propagates along the z axis. a) What is the magnitude and direction of the magnetic field? b) What is the frequency f? c) What is the angular frequency w? d) What is the wavenmber k?

Answer 1

Answer:

(a) 3.33 x 10^-7 T along Y axis

(b) 6 x 10^14 Hz

(c) 3.768 x 10^15 rad/s

(d) 2 x 10^6 m^-1

Explanation:

Wavelength = 500 nm = 500 x 10^-9 m

Electric Field, E = 100 i (along + X axis)

Wave is in +Z axis

So, the magnetic field is in + Y axis.

(a) c = E / B

B = E / c = 100 / (3 x 10^8) = 3.33 x 10^-7 T along Y axis

(b) Frequency = wave speed / wavelength = ( 3 x 10^8) / (500 x 10^-9)

frequency = 6 x 10^14 Hz

(c) w = 2 x 3.14 x f = 2 x 3.14 x 6 x 10^14 = 3.768 x 10^15 rad/s

(d) k = reciprocal of wavelength = 1 / (500 x 10^-9) = 2 x 10^6 m^-1