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 peak value of electric field at a point in electromagnetic wave is 15 V . `m^(-1)`, then average electrical energy density (in j . `m^(-3)`)