Select 4 out of next five problems. (13 x 4 =52 points) Extra credit for solving all.
14. (13 points) A plane electromagnetic sinusoidal wave of frequency 20.0 MHz travels in
free space in the negative z direction. At some point and at some instant, the electric field
has its maximum value of 200 N/C along the y-axis.
(a) What is the wavelength of the wave? (2)
$ \lambda = \frac{c}{f} = \frac{2.99772 \times 10^8}{20 \times 10^6} $
(b) Find the wave number and the angular frequency. (4)
$ k = 2 \pi f = 2 \pi / \lambda $
(c) Find the maximum value of the magnetic field. (2)
(d) Express $ \vec{E} $ and $ \vec{B} $ in a vector form as a function of space and time. (5)
