The magnetic field in a plane electromagnetic wave is given by
${B_y} = \left( {2 \times {{10}^{ - 7}}} \right)\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)T$
$(a)$ What is the wavelength and frequency of the wave?
$(b)$ Write an expression for the electric field.
The magnetic field in a plane electromagnetic wave is given by
${B_y} = \left( {2 \times {{10}^{ - 7}}} \right)\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)T$
$(a)$ What is the wavelength and frequency of the wave?
$(b)$ Write an expression for the electric field.
$(a)$ Comparing the given equation with
$B_{y}=B_{0} \sin \left[2 \pi\left(\frac{x}{\lambda}+\frac{t}{T}\right)\right]$
We get, $\lambda=\frac{2 \pi}{0.5 \times 10^{3}} m =1.26 \,m$
and $\quad \frac{1}{T}=v=\left(1.5 \times 10^{11}\right) / 2 \pi=23.9 \,GHz$
$(b)$ $E_{0}=B_{0} c=2 \times 10^{-7} \,T \times 3 \times 10^{8} \,m / s =6 \times 10^{1}\, V / m$
The electric field component is perpendicular to the direction of propagation and the direction of magnetic field. Therefore, the electric field component along the $z$ -axis is obtained as
$E_{z}=60 \sin \left(0.5 \times 10^{3} x+1.5 \times 10^{11} t\right)\, V / m$
Similar Questions
Find the direction of vibration of Electric field if vibration of magnetic field is in positive $x-$ axis and propagation of em wave is along positive $y-$ axis.
Find the direction of vibration of Electric field if vibration of magnetic field is in positive $x-$ axis and propagation of em wave is along positive $y-$ axis.
The average value of electric energy density in an electromagnetic wave is :
The average value of electric energy density in an electromagnetic wave is :
A radiation is emitted by $1000\, W$ bulb and it generates an electric field and magnetic field at $P$, placed at a distance of $2\, m$. The efficiency of the bulb is $1.25 \%$. The value of peak electric field at $P$ is $x \times 10^{-1} \,V / m$. Value of $x$ is. (Rounded-off to the nearest integer)
[Take $\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}$ $ms ^{-1}$ ]
A radiation is emitted by $1000\, W$ bulb and it generates an electric field and magnetic field at $P$, placed at a distance of $2\, m$. The efficiency of the bulb is $1.25 \%$. The value of peak electric field at $P$ is $x \times 10^{-1} \,V / m$. Value of $x$ is. (Rounded-off to the nearest integer)
[Take $\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}$ $ms ^{-1}$ ]
- [JEE MAIN 2021]
A radar sends an electromagnetic signal of electric field $\left( E _{0}\right)=2.25\,V / m$ and magnetic field $\left( B _{0}\right)=1.5 \times 10^{-8}\,T$ which strikes a target on line of sight at a distance of $3\,km$ in a medium After that, a pail of signal $(echo)$ reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time $t_{0}$ from radar. then after how much time (in $\times 10^{-5}\,s$) echo will reach to the radar?
A radar sends an electromagnetic signal of electric field $\left( E _{0}\right)=2.25\,V / m$ and magnetic field $\left( B _{0}\right)=1.5 \times 10^{-8}\,T$ which strikes a target on line of sight at a distance of $3\,km$ in a medium After that, a pail of signal $(echo)$ reflects back towards the radar vitli same velocity and by same path. If the signal was transmitted at time $t_{0}$ from radar. then after how much time (in $\times 10^{-5}\,s$) echo will reach to the radar?
- [JEE MAIN 2022]
Given below are two statements:
Statement $I$ : Electromagnetic waves are not deflected by electric and magnetic field.
Statement $II$ : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E _0=\sqrt{\frac{\mu_0}{\varepsilon_0}} B_0$
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement $I$ : Electromagnetic waves are not deflected by electric and magnetic field.
Statement $II$ : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E _0=\sqrt{\frac{\mu_0}{\varepsilon_0}} B_0$
In the light of the above statements, choose the correct answer from the options given below:
- [JEE MAIN 2023]