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:
- Εx = a + jb
- Εy = c + jd
- Εz = e + jf
Εmagnitude = g + jh = √ [(Εx)(Εx) + (Εy)(Εy) + (Εz)(Εz)]
Real Part {Εmagnitude} = g
Imaginary Part {Εmagnitude} = h
Magnitude {Εmagnitude} = sqrt [g*g + h*h]
All the above quantities (Εx, Εy, Εz, Εmagnitude ) are the rms (root mean square) values.
Let the unit vector of the normal to a surface/plane at the point of observation be {Nx, Ny, Nz}
The normal component of electric field is given by,
Εnormal = Nx*Εx + Ny*Εy + Nz*Εz = {(Nx*a+Ny*c+Nz*e) + j(Nx*b+Ny*d+Nz*f)} = m + jn
Magnitude {Εnormal} = √ [m*m + n*n]
Theoretically, on a conductor surface Εmagnitude = Εnormal. However, an insignificant difference (numerical noise) may exist between Εmagnitude and Εnormal. Therefore, Εmagnitude on a conductor surface is also the same as Εnormal.
In the model space at an observation point on an observation plane/surface, Εmagnitude is not equal to Εnormal. Therefore, in the model space at an observation point on an observation plane/surface, Εmagnitude is the rms value of the resultant magnitude of the electric field.