$A$ plane electromagnetic wave of frequency $20 \ MHz$ travels in free space along the $+x$ direction. At a particular point in space and time, the electric field vector of the wave is $E_y = 9.3 \ Vm^{-1}$. Then, the magnetic field vector of the wave at that point is:

$A$ carbon dioxide laser emits a sinusoidal electromagnetic wave that travels in a vacuum in the negative $x-$ direction. The wavelength is $10.6\,\mu m$ and the $\vec E$ field is parallel to the $z-$ axis,with $E_{max} = 1.5 \times 10^6\, V/m$. Then the vector equations for $\vec E$ and $\vec B$ as a function of time and position are:

If $c$ is the speed of electromagnetic waves in vacuum,its speed in a medium of dielectric constant $K$ and relative permeability $\mu_r$ is:

$A$ plane $EM$ wave travelling in vacuum along $z$-direction is given by $\vec E = E_0 \sin(kz - \omega t) \hat i$ and $\vec B = B_0 \sin(kz - \omega t) \hat j$.
$(i)$ Evaluate $\int \vec E \cdot d\vec l$ over the rectangular loop $1234$ shown in the figure.
$(ii)$ Evaluate $\int \vec B \cdot d\vec s$ over the surface bounded by loop $1234$.
$(iii)$ Use $\int \vec E \cdot d\vec l = -\frac{d\phi_E}{dt}$ to prove $\frac{E_0}{B_0} = c$.
$(iv)$ By using a similar process and the equation $\int \vec B \cdot d\vec l = \mu_0 I + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$,prove that $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

$A$ light beam is described by $E = 800 \sin \omega (t - x/c)$. An electron is allowed to move normal to the propagation of the light beam with a speed of $3 \times 10^{7} \text{ m/s}$. What is the maximum magnetic force exerted on the electron?

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