The electric field component of an electromagnetic wave is expressed as $$\mathbf{E}=(3\hat{\mathbf{j}}+b\hat{\mathbf{k}})\times10^{-3}\sin\left[10^7(x+2y+3z-\beta t)\right]$$ in SI units. Taking $$c=3\times10^8\ \text{m}/\text{s}$$ as the speed of electromagnetic wave in vacuum, choose the correct options.

A

The value of constant $$\beta$$ is $$\beta=3\times10^8\sqrt{14}$$

B

The value of constant $$b$$ is $$b=2$$

C

The average energy density of the electromagnetic wave is $$U=6.5\times10^{-6}\varepsilon_0$$ in SI units

D

The amplitude of magnetic field is $$B=1.20\times10^{-11}\ \text{T}$$