Write characteristics of electromagnetic waves. 

The magnetic field of a plane electromagnetic wave is given by

$\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T$ The amplitude of the electric field would be.

An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of that antenna is $5.0\, mm$. it can radiate a signal of minimum frequency of $GHz .$

(Given $\mu_{ r }=1$ for dielectric medium)

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.

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by ${E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .$ The dielectric constant of the medium is equal to :

(Take $\mu_{{r}}=1$ )