Significance of resultant magnitude of the electric field in COULOMB for phasor mode of operation.
Dr. K.M. Prasad - Senior Application Engineer
Software: Coulomb™
In COULOMB, when the Operation Mode is set to Phasor (Single Frequency). The electric field components will be phasors viz:
- Ε_{x} = a + jb
- Ε_{y} = c + jd
- Ε_{z} = e + jf
Ε_{magnitude} = g + jh = √ [(Ε_{x})(Ε_{x}) + (Ε_{y})(Ε_{y}) + (Ε_{z})(Ε_{z})]
Real Part {Ε_{magnitude}} = g
Imaginary Part {Ε_{magnitude}} = h
Magnitude {Ε_{magnitude}} = sqrt [g*g + h*h]
All the above quantities (Ε_{x}, Ε_{y}, Ε_{z}, Ε_{magnitude} ) are the rms (root mean square) values.
Let the unit vector of the normal to a surface/plane at the point of observation be {N_{x}, N_{y}, N_{z}}
The normal component of electric field is given by,
Ε_{normal} = N_{x}*Ε_{x} + N_{y}*Ε_{y} + N_{z}*Ε_{z} = {(N_{x}*a+N_{y}*c+N_{z}*e) + j(N_{x}*b+N_{y}*d+N_{z}*f)} = m + jn
Magnitude {Ε_{normal}} = √ [m*m + n*n]
Theoretically, on a conductor surface Ε_{magnitude} = Ε_{normal}. However, an insignificant difference (numerical noise) may exist between Ε_{magnitude} and Ε_{normal}. Therefore, Ε_{magnitude} on a conductor surface is also the same as Ε_{normal}.
In the model space at an observation point on an observation plane/surface, Ε_{magnitude} is not equal to Ε_{normal}. Therefore, in the model space at an observation point on an observation plane/surface, Ε_{magnitude} is the rms value of the resultant magnitude of the electric field.