Total energy per unit area of a EM pulse

This result assumes that the Poynting vector is time-independent and that the electric potential is zero.
  • #1
TheTourist
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B=Boexp[-(kz-ωt)2)] i(hat)

Calculate the electric field associated with the above magnetic field pulse.
Calculate the Poynting vector for the EM field and the total energy per unit area.
Use Maxwell's equations in vacuum and assume electric potential is zero.


Homework Equations


N=(1/μo)*EXB
Amperes Law



I calculated the electric field to be E=Boc*exp[-(kz-ωt)2] j(hat)
And the Poynting vector to be
N=-(Bo2c/μo)*exp[-(kz-ωt)2] k(hat)

I am stuck on how to calculate the the energy per unit area. I think I would have to integrate over time (t=0 to t=∞) at some fixed point but I'm not sure.
 
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  • #2
Any help would be appreciated. The total energy per unit area is given by the integral of the Poynting vector over all space,Energy/Area = 1/μo ∫-∞∞ Boc2 exp[-(kz-ωt)2] dzwhich can be evaluated as Energy/Area = (Boc2/2μok)*(1-erf(√2kz))where erf is the error function.
 

What is total energy per unit area of an EM pulse?

The total energy per unit area of an EM pulse, also known as intensity, is a measure of the amount of energy passing through a unit area perpendicular to the direction of propagation of the pulse. It is usually measured in joules per square meter (J/m^2).

How is the total energy per unit area of an EM pulse calculated?

The total energy per unit area of an EM pulse can be calculated by multiplying the electric field strength by the magnetic field strength and dividing by the impedance of free space (377 ohms). This equation is represented as: I = (E^2/mu_0) * (1/Z_0), where I is the intensity, E is the electric field strength, mu_0 is the permeability of free space, and Z_0 is the impedance of free space.

What factors affect the total energy per unit area of an EM pulse?

The total energy per unit area of an EM pulse can be affected by several factors, including the amplitude of the electric and magnetic fields, the frequency of the pulse, the distance from the source, and the medium through which the pulse is traveling. Additionally, the polarization and direction of the pulse can also affect its intensity.

What is the relationship between total energy per unit area and power of an EM pulse?

The total energy per unit area of an EM pulse is directly proportional to the power of the pulse. This means that as the intensity increases, so does the power. The relationship between the two can be described by the equation: P = I * A, where P is power, I is intensity, and A is the area through which the pulse is passing.

Why is the total energy per unit area of an EM pulse important?

The total energy per unit area of an EM pulse is an important measure in understanding the behavior and effects of electromagnetic radiation. It is used in various fields, such as telecommunications, astronomy, and medicine, to determine the strength and potential impact of EM pulses. It is also a crucial factor in determining safety guidelines and regulations for exposure to EM radiation.

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