Suppose that intensity of a laser is $\left(\frac{315}{\pi}\right)\, W / m ^{2} .$ The $rms$ electric field, in units of $V / m$ associated with this source is close to the nearest integer is $\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)$

Suppose that the electric field part of an electromagnetic wave in vacuum is

$E =\left\{(3.1 \;N / C ) \text { cos }\left[(1.8 \;rad / m ) y+\left(5.4 \times 10^{6} \;rad / s \right) t\right]\right\} \hat{ i }$

$(a)$ What is the direction of propagation?

$(b)$ What is the wavelength $\lambda$ ?

$(c)$ What is the frequency $v ?$

$(d)$ What is the amplitude of the magnetic field part of the wave?

$(e)$ Write an expression for the magnetic field part of the wave.

The electric field of a plane polarized electromagnetic wave in free space at time $t = 0$ is given by an expression

$\vec E(x,y) = 10\hat j\, cos[(6x + 8z)]$

The magnetic field $\vec B (x,z, t)$ is given by : ($c$ is the velocity of light)

For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is

$\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T$

The instantaneous electric field $\overrightarrow{ E }$ corresponding to $\overrightarrow{ B }$ is : (speed of light $\left.c=3 \times 10^{8} ms ^{-1}\right)$

A plane electromagnetic wave travels in free space along the $x -$ direction. The electric field component of the wave at a particular point of space and time is $E =6\; Vm^{-1}$ along $y -$ direction. Its corresponding magnetic filed component, $B$ would be

If radiation is totally absorbed and energy incident on surface in time $t$ be $U$ then write equation of momentum imparted to surface.