Answer
(a) $B_0 = 3.3\times 10^{-6}~T$
(b) $B = 1.7\times 10^{-6}~T$
B points to the left.
Work Step by Step
(a) We can find the magnetic field amplitude:
$B_0 = \frac{E_0}{c}$
$B_0 = \frac{1000~V/m}{3.0\times 10^8~m/s}$
$B_0 = 3.3\times 10^{-6}~T$
(b) We can find the magnetic field strength:
$B = \frac{E}{c}$
$B = \frac{500~V/m}{3.0\times 10^8~m/s}$
$B = 1.7\times 10^{-6}~T$
To find the direction of the electromagnetic wave, we can find $E \times B$
To apply the right hand rule to electromagnetic waves, the thumb points in the direction of the electric field, the index finger points in the direction of the magnetic field, and the palm faces toward the direction of the wave's motion.
If the palm faces into the page, and the thumb points straight down in the -y direction, then the index finger points to the left in the -x direction
B points to the left.
