The electric field of an electromagnetic wave in free space is given by $\vec E$$=10 cos (10^7t+kx)$$\hat j$ $volt/m $ where $t$ and $x$ are in seconds and metres respectively. It can be inferred that
$(1)$ the wavelength $\lambda$ is $188.4\, m.$
$(2)$ the wave number $k$ is $0.33\,\, rad/m.$
$(4)$ the wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct ?
$(3)$ and $(4)$
$(1)$ and $(2)$
$(2)$ and $(3)$
$(1)$ and $(3)$
A metal sample carrying a current along $X-$ axis with density $J_x$ is subjected to a magnetic field $B_z$ ( along $z-$ axis ). The electric field $E_y$ developed along $Y-$ axis is directly proportional io $J_x$ as well as $B_z$ . The constant of proportionality has $SI\, unit$.
An electromagnetic wave of frequency $1\times10^{14}\, hertz$ is propagating along $z-$ axis. The amplitude of electric field is $4\, V/m$ . lf ${\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2$ , then average energy density of electric field will be:
Intensity of sunlight is observed as $0.092\, {Wm}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point? $\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.$ )
Give equation which relate $c,{\mu _0},{ \in _0}$.
The velocity of electromagnetic radiation in a medium of permittivity ${\varepsilon _0}$ and permeability ${\mu _0}$ is given by