The electric field of a plane electromagnetic wave in vacuum is...

Given, $\vec{E} = 30 \sin \left(6\pi \times 10^{10} t - 200\pi x\right) \hat{j} \text{ V/m}$

Comparing with the standard equation $\vec{E} = E_0 \sin(\omega t - k x) \hat{j}$, we get:
$E_0 = 30 \text{ V/m}$
$\omega = 6\pi \times 10^{10} \text{ rad/s}$

The amplitude of the magnetic field is:
$B_0 = \dfrac{E_0}{c} = \dfrac{30}{3 \times 10^8} = 10^{-7} \text{ T}$

The frequency of the electromagnetic wave is:
$f = \dfrac{\omega}{2\pi} = \dfrac{6\pi \times 10^{10}}{2\pi} = 3 \times 10^{10} \text{ Hz}$

A frequency of $3 \times 10^{10} \text{ Hz}$ falls in the range of Microwaves (which typically span from $10^9 \text{ Hz}$ to $3 \times 10^{11} \text{ Hz}$).

Answer: $10^{-7} \text{ T}$, Microwaves