The electric field part of an electromagnetic wave in vacuum is

$E = 3.1\,NC^{-1}\,cos\,[\,(1.8\,rad\,m^{-1})\,y + (5.4\times 18^8\,rad\,s^{-1})\,t\,]\,\hat i$

The wavelength of this part of electromagnetic wave is......$m$

The electric field of a plane electromagnetic wave is given by $\vec E = {E_0}\hat i\,\cos \,\left( {kz} \right)\,\cos \,\left( {\omega t} \right)$ The corresponding magnetic field $\vec B$ is then given by

A plane electromagnetic wave of frequency $20\,MHz$ propagates in free space along $x$-direction. At a particular space and time, $\overrightarrow{ E }=6.6 \hat{ j } V / m$. What is $\overrightarrow{ B }$ at this point?

A charged particle oscillates about its mean equilibrium position with a frequency of $10^9\ Hz$. The electromagnetic waves produced:

In propagation of electromagnetic waves the angle between the direction of propagation and plane of polarisation is

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.