Light is an electromagnetic wave. Its speed in vacuum is given by the expression

The oscillating electric and magnetic vectors of an electromagnetic wave are oriented along

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $\overrightarrow{ u }_1=4 \hat{ i } ms ^{-1}$, enters a region of uniform static magnetic field normal to the $x-y$ plane. The region of the magnetic field extends from $x=0$ to $x$ $=L$ for all values of $y$. After passing through this region, the particle emerges on the other side after $10$ milliseconds with a velocity $\overline{ u }_2=2(\sqrt{3} \hat{ i }+\hat{ j }) ms ^{-1}$. The correct statement$(s)$ is (are) :

$(A)$ The direction of the magnetic field is $-z$ direction.

$(B)$ The direction of the magnetic field is $+z$ direction

$(C)$ The magnitude of the magnetic field $\frac{50 \pi M }{3 Q }$ units.

$(D)$ The magnitude of the magnetic field is $\frac{100 \pi M}{3 Q}$ units.

Wavelength of light of frequency $100\;Hz$

An electromagnetic wave of frequency $1\times10^{14}\, hertz$ is propagating along $z-$ axis. The amplitude of electric field is $4\, V/m$ . lf ${\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2$ , then average energy density of electric field will be: