Question

3. The magnetic field of an electromagnetic wave is given as B-3uT sin( 1x10' x -2xfi) where r is in meters. a) Calculate wavelength and frequency. b) Calculate the energy of one photon, in Joules and in eV c) Calculate the electric field amplitude.

Answer 1

As per the equation of the magnetic field of electromagnetic wave

$B_z = 3\mu T Sin(1*10^7x-2\pi ft)$

standard equation of the magnetic field of electromagnetic wave is

$B_z = B_0 Sin[2\pi((\frac{x}{\lambda }) +( \frac{t}{T}))]$

on comparing given equation with standard equation we have

2m( 1 * 1072.

$\frac{2\pi}{1*10^7 }= \lambda$

$\lambda= 6.283*10^{-7} m$

frequency of the wave can be calculated by

$v = \frac{c}{\lambda}= \frac{3*10^{8}}{6.283*10^{-7}} Hz$

------------------------- Solution of part b ----------------

Energy of photon is given by

or

$E = \frac{3.164*10^{-19}} {1.602*10^{-19}} eV$

----------------- Solution of part C ---------------------------

To calculate the electric field amplitude we have