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?

(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