Speed of electromagnetic radiation in vacuum is

English

Gujarati

Hindi

8.Electromagnetic waves

easy

The speed of electromagnetic radiation in vacuum is

${\mu _0}{ \in _0}$

$\sqrt {{\mu _0}{ \in _0}} $

$\frac{1}{{{\mu _0}{ \in _0}}}$

$\frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$

Solution

Maxwell deduced that the speed of propagation of an electromagnetic wave through a vacuum is entirely determined by the constants $\mu_0$ and $\epsilon_0$ as the following:

$c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$

We know that $\mu_0=4 \pi \times 10^{-7}\,Ns ^2 C ^{-2}$ and $\epsilon_0=8.854 \times 10^{-12}\, C ^2\, N ^{-1} \,m ^{-2}$ which gives:

$c =\frac{1}{\sqrt{4 \pi \times 10^{-7} 8.854 \times 10^{-1.12}}}=2.998 \times 10^8\,m / s$

Standard 12

Physics

Write magnitude and dimensional formula of $\frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$

medium

The electric field in a plane electromagnetic wave is given by

$\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}$

If this wave falls normally on a perfectly reflecting surface having an area of $100 \;{cm}^{2}$. If the radiation pressure exerted by the $E.M.$ wave on the surface during a $10\, minute$ exposure is $\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}$. Find the value of ${x}$.

hard

(JEE MAIN-2021)

The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_0 \cos (\omega t-k z) \hat{i}$.The corresponding magnetic induction vector will be :

hard

(JEE MAIN-2024)

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