Calculating SAR from multiple sources

[Wotwot]

The Specific Absorption Rate (the rate at which energy is absorbed by a unit mass) given in W/kg is calculated by the following equation

SAR = (sigma * Erms^2) / p

Where sigma is the conductivity of the material (given in S/m), Erms is the RMS electric field (V/m) at the location and p is the density of the material (kg/m^3)

If there were multiple sources radiating the body from different places, all of them with the same frequency, and I wanted to calculate the total SAR at a specific location within the body, how would I go about doing that?
I have three options here.

1) Calculate the total electric field at the location and then calculate its RMS value and use it in the above equation

2) Calculate the SAR due to each source separately by using the Erms values due to each source and then add all the SAR values together

3) Add all the Erms values due to all the sources together and use this new Erms value in the above equation to find SAR

The above two methods give two different answers because of the fact that:

(a+b)^2 is not the same as (a^2 + b^2)

Does my choice of method change if all the sources have different frequencies?

 

[siriwat007]

As electric field is a vector quantity, it can be either constructive or destructive at a particular point if radiated from two or more sources. So, the method 1) will give the right SAR amount.