If the electric field of a plane electromagne | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given electric field is $E_z = 60 \sin(0.5 	imes 10^3 x + 1.5 	imes 10^{11} t) \ Vm^{-1}$.Comparing this with the standard equation $E_z = E

Vedclass · Accepted Answer

$B_y = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 x + 1.5 	imes 10^{11} t) \ T$

Vedclass · Answer

(A) The given electric field is $E_z = 60 \sin(0.5 	imes 10^3 x + 1.5 	imes 10^{11} t) \ Vm^{-1}$.Comparing this with the standard equation $E_z = E_0 \sin(kx + \omega t)$,we get $E_0 = 60 \ Vm^{-1}$.The amplitude of the magnetic field $B_0$ is given by $B_0 = \frac{E_0}{c}$,where $c = 3 	imes 10^8 \ ms^{-1}$ is the speed of light.$B_0 = \frac{60}{3 	imes 10^8} = 20 	imes 10^{-8} = 2 	imes 10^{-7} \ T$.Since the wave propagates in the negative $x$-direction (indicated by the $+kx$ term) and the electric field is in the $z$-direction,the magnetic field must be in the $y$-direction to satisfy the direction of propagation $\vec{E} 	imes \vec{B} \propto \vec{v}$.Specifically,$\hat{k} 	imes \hat{i} = \hat{j}$ (for propagation in $-x$,$\hat{E} 	imes \hat{B} = -\hat{i}$,so $\hat{k} 	imes \hat{j} = -\hat{i}$).Thus,the magnetic field is $B_y = B_0 \sin(kx + \omega t) = 2 	imes 10^{-7} \sin(0.5 	imes 10^3 x + 1.5 	imes 10^{11} t) \ T$.

If the electric field of a plane electromagnetic wave is $E_z = 60 \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) \ Vm^{-1}$,then the magnetic field of the wave is

Similar Questions

If $\vec E$ and $\vec B$ represent the electric and magnetic field vectors of an electromagnetic wave,then the direction of propagation of the electromagnetic wave is in the direction of

$A$ plane electromagnetic wave travelling along the $X$-direction has a wavelength of $3 \ mm$. The variation in the electric field occurs in the $Y$-direction with an amplitude of $66 \ Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively:

The electric and the magnetic field,associated with an electromagnetic wave propagating along the $+z$-axis,can be represented by

In a plane $EM$ wave,the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \,Hz$ and an amplitude of $50 \,Vm^{-1}$. The total average energy density of the electromagnetic field of the wave is :
[Use $\varepsilon_0 = 8.85 \times 10^{-12} \,C^2 / Nm^2$ ]

The magnetic field in a travelling electromagnetic wave has a peak value of $20 \ nT$. The peak value of electric field strength is ...... $Vm^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module