Near Field Coordinate Systems (FE card)

The coordinate systems for the FE card have specific definitions/conventions. Use the appropriate coordinate system for the application.

Cartesian coordinates x, y, z



Figure 1. Field calculation in the Cartesian coordinate system.

Observation point:

(1) r=[ x y z ]

Unit vectors of the coordinate system:

(2) x ^ =[ 1 0 0 ]         y ^ =[ 0 1 0 ]         z ^ =[ 0 0 1 ]

Cylindrical coordinates around Z 軸 ρ , φ , z



Figure 2. Field calculation in the Cylindrical coordinate system.

Observation point:

(3) r=[ ρcosφ ρsinφ z ]

Unit vectors of the coordinate system:

(4) ρ ^ =[ cosφ sinφ 0 ]         φ ^ =[ sinφ cosφ 0 ]         z ^ =[ 0 0 1 ]

Spherical coordinates r , ϑ , φ



Figure 3. Field calculation in the spherical coordinate system.

Observation point:

(5) r=[ rsinϑcosφ rsinϑsinφ rcosϑ ]

Unit vectors of the coordinate system:

(6) r ^ =[ sinϑcosφ sinϑsinφ cosϑ ]         ϑ ^ =[ cosϑcosφ cosϑsinφ sinϑ ]         φ ^ =[ sinφ cosφ 0 ]

Cylindrical coordinates around X 軸 r , φ , x



Figure 4. Field calculation in the Cylindrical coordinate system around the X 軸.

Observation point:

(7) r=[ x ρcosφ ρsinφ ]

Unit vectors of the coordinate system:

(8) ρ ^ =[ 0 cosφ sinφ ]         φ ^ =[ 0 sinφ cosφ ]         x ^ =[ 1 0 0 ]

Cylindrical coordinates around Y 軸 r , φ , y



Figure 5. Field calculation in the Cylindrical coordinate system around the Y 軸.

Observation point:

(9) r=[ ρcosφ y ρsinφ ]

Unit vectors of the coordinate system:

(10) ρ ^ =[ cosφ 0 sinφ ]         φ ^ =[ sinφ 0 cosφ ]         y ^ =[ 0 1 0 ]

Conical coordinates around the Z 軸 φ , z



Figure 6. Field calculation in the Conical coordinate system.

This option is similar to the field calculation in cylindrical coordinates around the Z 軸, where the radius r changes with the height z :

(11) r(z)= r 0 + Δr Δz (z z 0 )
where z is within the range z 0 z 0 + n z Δz .

Observation point:

(12) r=[ ( r 0 + Δr Δz (z z 0 ) )cosφ ( r 0 + Δr Δz (z z 0 ) )sinφ z ]

Unit vectors of the coordinate system:

(13) r ^ =[ cosφ sinφ 0 ]         φ ^ =[ sinφ cosφ 0 ]         z ^ =[ 0 0 1 ]