Given the electric field expression:

$E_z = 300 \sin(5\pi \times 10^3 x - 3\pi \times 10^{11} t) \, \text{Vm}^{-1}$

The amplitude of the electric field ($E_0$) is $300 \, \text{V/m}$.

The velocity ($v$) of the wave in the medium is given by the ratio of the coefficients of time and displacement in the wave equation, which can be calculated as:

$v = \frac{\text{Coefficient of } t}{\text{Coefficient of } x} = \frac{3\pi \times 10^{11}}{5\pi \times 10^3} = \frac{3}{5} \times 10^8 \, \text{m/s}$

The relationship between the electric field amplitude and the magnetic field amplitude in an electromagnetic wave is given by:

$B_0 = \frac{E_0}{v}$

Substituting the values for $E_0$ and $v$ into this formula:

$B_0 = \frac{300}{\frac{3}{5} \times 10^8}$

$B_0 = \frac{300 \times 5}{3 \times 10^8}$

$B_0 = \frac{1500}{3 \times 10^8}$

$B_0 = 5 \times 10^{-6} \, \text{T}$

Therefore, the amplitude of the magnetic field ($B_0$) is $5 \times 10^{-6}$ T.