Power loss in sinusoidal electric fields

In summary, the equation for average power dissipation per unit volume in electromagnetics is P=(1/2)*J*E (W/m^3). The coefficient of 1/2 comes from the fact that previously, the differential power dissipation was given as dP= J*E (W/m^3) and now it is based on the peak value of a sinusoid. This is represented by the value of Erms ^ 2, which gives the coefficient of 1/2 in the equation.
  • #1
JerryG
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0

Homework Statement


In my electromagnetics book, in the section that talks about loss tangents, the equation for average power dissipation per unit volume is P=(1/2)*J*E (W/m^3). What does the coefficient of 1/2 come from? Earlier in the book, it gave the differential power dissipation dP= J*E (W/m^3)

Homework Equations


J = current density.
E= electric field.
 
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  • #2
Is it possible that previously E was a constant value, and now E is the peak value of a sinusoid?
 
  • #3
gneill said:
Is it possible that previously E was a constant value, and now E is the peak value of a sinusoid?

That's it. It's the Erms ^ 2 that gives the 1/2.
 

1. What causes power loss in sinusoidal electric fields?

The primary cause of power loss in sinusoidal electric fields is resistance. As electric current flows through a material with resistance, some of the energy is converted into heat, resulting in a loss of power. Other factors that can contribute to power loss include skin effect, proximity effect, and dielectric losses.

2. How does frequency affect power loss in sinusoidal electric fields?

As frequency increases, power loss in sinusoidal electric fields also increases. This is due to the skin and proximity effects, which cause the current to be concentrated near the surface of the conductor at higher frequencies. This results in more resistance and therefore more power loss.

3. Is there a way to reduce power loss in sinusoidal electric fields?

Yes, there are several ways to reduce power loss in sinusoidal electric fields. One method is to use materials with lower resistance, such as copper instead of aluminum. Another way is to increase the size of the conductor, which reduces the overall resistance. Additionally, using materials with higher conductivity or utilizing special coatings can also help reduce power loss.

4. How does the length of the conductor affect power loss in sinusoidal electric fields?

The longer the conductor, the higher the power loss in sinusoidal electric fields. This is because as the length of the conductor increases, so does its resistance. This is why power lines, which can be several miles long, often use high-voltage transmission to reduce power loss.

5. Can power loss in sinusoidal electric fields be measured?

Yes, power loss in sinusoidal electric fields can be measured using various methods such as the two-wattmeter method or the three-voltmeter method. These techniques involve measuring the voltage and current at different points in the circuit and using mathematical formulas to calculate the power loss. Other methods, such as using specialized equipment like power analyzers, can also be used to measure power loss.

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