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.

A radar sends an electromagnetic signal of electric field $\left( E _{0}\right)=2.25\,V / m$ and magnetic field $\left( B _{0}\right)=1.5 \times 10^{-8}\,T$ which strikes a target on line of sight at a distance of $3\,km$ in a medium After that, a pail of signal $(echo)$ reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time $t_{0}$ from radar. then after how much time (in  $\times 10^{-5}\,s$) echo will reach to the radar?

A plane electromagnetic wave of wavelength $\lambda $ has an intensity $I.$  It is propagating along the positive $Y-$  direction. The allowed expressions for the electric and magnetic fields are given by

The magnetic field of a beam emerging from a filter facing a floodlight is given by B${B_0} = 12 \times {10^{ - 8}}\,\sin \,(1.20 \times {10^7}\,z - 3.60 \times {10^{15}}t)T$. What is the average intensity of the beam ?

A long straight wire of resistance $R$, radius $a $ and length $ l$ carries a constant current $ I.$ The Poynting vector for the wire will be

Write equation of energy density of electromagnetic waves.