What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristic of $LASER$ beam is responsible for the constant intensity which is missing in the case of light from the bulb ?
Intensity of waves is inversely proportional to source of distance from source $\left(\because\right.$ I $\left.\propto \frac{1}{r^{2}}\right)$ when distance become double then intensity become $\frac{1}{4}^{\text {th }}$ value they do not spread hence here inten sity remains same.
Following geometric characteristics of LASER beam are responsible for constant intensity,
$(i)$ Unidirectional
$(ii)$ Monochromatic
$(iii)$ Coherent light
$(iv)$ Highly collimated
These characteristics are absent in case of bulb in given case.
The electric field of a plane electromagnetic wave is given by $\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )$ Its magnetic field will be given by
Pointing vectors $\vec S$ is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically, it is given by $\vec S = \frac{1}{{{\mu _0}}}(\vec E \times \vec B)$. Show the nature of $\vec S$ vs $t$ graph.
Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is $2.0$ . The relative permittivity will be :
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.\overrightarrow {dl} } $ over the rectangular loop $1234$ shown in figure.
$(ii)$ Evaluate $\int {\vec B} .\overrightarrow {ds} $ over the surface bounded by loop $1234$.
$(iii)$ $\int {\vec E.\overrightarrow {dl} = - \frac{{d{\phi _E}}}{{dt}}} $ to prove $\frac{{{E_0}}}{{{B_0}}} = c$
$(iv)$ By using similar process and the equation $\int {\vec B} .\overrightarrow {dl} = {\mu _0}I + { \in _0}\frac{{d{\phi _E}}}{{dt}}$ , prove that $c = \frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$
The speed of electromagnetic wave in a medium (whose dielectric constant is $2.25$ and relative permeability is $4$ ) is equal to .......... $\times 10^8 \,m / s$