How Is Electric Field Amplitude Related to Power in Electromagnetic Waves?

[Tcat]

Hi I am having trouble relating power to the electric field amplitude, I know that P=IA and E=cB, could someone please help? The problem reads:

What electric-field amplitude is required to transmit an amount of power equal to that handled by modern transmission lines (that carry voltages and currents of 500 kV and 1000 A)? Suppose power is to be transmitted in a beam of cross-sectional area 100m^2.

 

[Astronuc]

See if these help:

http://physics.bu.edu/~duffy/PY106/EMWaves.html

http://www.osha.gov/SLTC/radiofrequencyradiation/electromagnetic_fieldmemo/electromagnetic.html

http://farside.ph.utexas.edu/teaching/302l/lectures/node102.html

 

[quicknote]

The relationship between power and electric field amplitude can be understood by considering the equation P=IA, where P represents power, I represents current, and A represents the cross-sectional area. In the case of electromagnetic waves, the power is carried by the electric and magnetic fields propagating through space.

To determine the required electric field amplitude for transmitting the given amount of power, we can rearrange the equation P=IA to solve for E, the electric field amplitude. This gives us E = P/(IA). Substituting the values given in the problem, we get E = (500 kV)(1000 A)/(100m^2) = 5 MV/m.

This means that the electric field amplitude required to transmit the given amount of power is 5 million volts per meter. It is important to note that this is a simplified calculation and in reality, factors such as losses and efficiency of the transmission line would need to be taken into account.

Furthermore, the equation E=cB is known as the electromagnetic wave equation and describes the relationship between the electric field (E), the speed of light (c), and the magnetic field (B). This equation is used to calculate the strength of the electric field in an electromagnetic wave.

I hope this explanation helps to clarify the relationship between power and electric field amplitude in the context of electromagnetic waves. If you have any further questions, please feel free to ask.