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Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field `vecE` and magnetic field `vecB` form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since `in_0` and `mu_0` are permittivity and permeability of free space, the velocity of electromagnetic wave, `c=(in_0 mu_0)^(-1//2)`. Energy density i.e., energy in unit volume due to electric field at any point, `u_E=1/2in_0E^2` Similarly, energy density due to magnetic field , `u_M=1/(2mu_0)B^2`. If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively.
`E=E_0sin(omegat-kx)` and `B=B_0sin(omegat-kx)`
Here, the frequency and the wavelength of oscillating electric and magnetic fields are `f=omega/(2pi)` and `lambda=(2pi)/k` respectively. Thus `E_"rms"=E_0/sqrt2` and `B_"rms"=B_0/sqrt2`, where `E_0/B_0=c`. Therefore, average energy density `baru_E=1/2in_0E_"rms"^2` and `baru_M=1/(2mu_0)B_"rms"^2`. The intensity of the electromagnetic wave at a point, `I=cbaru=c(baru_E+baru_B)`.
To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, `c=3xx10^8 m.s^(-1)` and `mu_0=4pixx10^(-7) H.m^(-1)`
Average energy density (in J . `m^(-3)` )of electromagnetic wave at that point

A

`4.98xx10^(-9)`

B

`9.95xx10^(-9)`

C

`4.98xx10^(-10)`

D

`9.95xx10^(-10)`

Text Solution

Verified by Experts

The correct Answer is:
D
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  • Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) Relation between omega and k

    A
    `omega=ck`
    B
    `omega=(ck)/(2pi)`
    C
    `omega=c/k`
    D
    `omega=c/(2pik)`

  • Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) if the wavelength is 1000Å, then the frequency (in Hz)

    A
    `10^13`
    B
    `3xx10^13`
    C
    `10^15`
    D
    `3xx10^15`

  • Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) If the electromagnetic wave propagates along x-axis, then the electric field vecE will be

    A
    along y-axis
    B
    along z-axis
    C
    on xy-plane
    D
    on yz-plane

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    Electromagnetic waves propagate through free space or a medium as transverse waves. The electric and magnetic fields are perpendicular to each other as well as perpendicular to the direction of propagation of waves at each point. In the direction of wave propagation, electric field vecE and magnetic field vecB form a right-handed cartesian coordinate system. During the propagation of electromagnetic wave, total energy of electromagnetic wave is distributed equally between electric and magnetic fields. Since in_0 and mu_0 are permittivity and permeability of free space, the velocity of electromagnetic wave, c=(in_0 mu_0)^(-1//2) . Energy density i.e., energy in unit volume due to electric field at any point, u_E=1/2in_0E^2 Similarly, energy density due to magnetic field , u_M=1/(2mu_0)B^2 . If the electromagnetic wave propagates along x-direction, then the equations of electric and magnetic field are respectively. E=E_0sin(omegat-kx) and B=B_0sin(omegat-kx) Here, the frequency and the wavelength of oscillating electric and magnetic fields are f=omega/(2pi) and lambda=(2pi)/k respectively. Thus E_"rms"=E_0/sqrt2 and B_"rms"=B_0/sqrt2 , where E_0/B_0=c . Therefore, average energy density baru_E=1/2in_0E_"rms"^2 and baru_M=1/(2mu_0)B_"rms"^2 . The intensity of the electromagnetic wave at a point, I=cbaru=c(baru_E+baru_B) . To answer the following questions , we assume that in case of propagation of electromagnetic wave through free space, c=3xx10^8 m.s^(-1) and mu_0=4pixx10^(-7) H.m^(-1) Intensity (in W . m^(-2) ) of electromagnetic wave at that point is almost

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