## 4 Analysis of Magnetic Field from 400 kV AC Power Transmission Line
The location of point M with respect to the ground is \(y_{0}=y_{\text{M}}\)  
Figure 2: Components of the magnetic field vectors at the point M.  
The vectors of the magnetic field strength generated at point M are \(H_{in}\) and \(H_{in}^{*}\) (\(i\) = A, B, C) (\(n\) = 1, 2). After distributing the directions of \(x\) and \(y\) axes, the following is obtained:  
\[H_{x}=H_{\text{A1}x}+H_{\text{B1}x}+H_{\text{C1}x}+H_{\text{A2}x}+H_{\text{B2}x }+H_{\text{C2}x}+H_{\text{A1}x}^{*}+H_{\text{B1}x}^{*}+H_{\text{C1}x}^{*}+H_{ \text{A2}x}^{*}+H_{\text{B2}x}^{*}+H_{\text{C2}x}^{*}, \tag{6}\]  
\[H_{y}=H_{\text{A1}y}+H_{\text{B1}y}+H_{\text{C1}y}+H_{\text{A2}y}+H_{\text{B2 }y}+H_{\text{C2}y}+H_{\text{A1}y}^{*}+H_{\text{B1}y}^{*}+H_{\text{C1}y}^{*}+H_{ \text{A2}y}^{*}+H_{\text{B2}y}^{*}+H_{\text{C2}y}^{*}. \tag{7}\]  
Assuming that constituents of the magnetic field strength vectors at the observation point M are as follows,  
\[E_{\text{M}inx}=\sqrt{\frac{1}{T}\sum_{i=1}^{n}E_{\text{M}inx\,\text{max}}^{2}} \tag{8}\]  
\[E_{\text{M}iny}=\sqrt{\frac{1}{T}\sum_{i=1}^{n}E_{\text{M}iny\,\text{max}}^{2}} \tag{9}\]  
the effective value of magnetic field strength at observation point M \(H_{\text{M}}\) is calculated using Equation (5). One millionth of a Tesla (1 \(\upmu\)T) corresponds to 0.8 A/m. As initial phases of conductors in the double-circuit symmetric 400 kV overhead power line are different by 120\({}^{0}\), the total magnetic field will be a rotating one, and for the magnetic field vector, at any observation point M, the time course will define an ellipse in a general way. The normal value of the rotating magnetic field strength is assumed to be the effective value of the sinusoid, the amplitude of which is equal to the semi-major axis of the ellipse orbited by the strength vector at the given point. To express respective constituents of the magnetic field strength (see Figure 2), the following markings are introduced: coordinate \(y\) of point M, \(y_{\text{M}}\); height of the conductors above the ground surface, \(y_{\text{A1}}=y_{\text{A2}}\), \(y_{\text{B1}}=y_{\text{B2}}\), \(y_{\text{C1}}=y_{\text{C2}}\). The phase reflections A\({}_{1}^{*}\), B\({}_{1}^{*}\), C\({}_{1}^{*}\), A\({}_{2}^{*}\), B\({}_{2}^{*}\), C\({}_{2}^{*}\) are situated at the same distances above the ground surface in the direction of the \(y\) axis. The distances from the conductors to the point M in the direction of the \(x\) axis are as follows:  
1. \(x_{\text{A1M}}=x_{\text{A1}}+x_{\text{M}}\) is the distance from phase A\({}_{1}\) to point M;
2. \(x_{\text{B1M}}=x_{\text{B1}}+x_{\text{M}}\) is the distance from phase B\({}_{1}\) to point M;
3. \(x_{\text{C1M}}=x_{\text{C1}}+x_{\text{M}}\) is the distance from phase C\({}_{1}\) to point M;
4. \(x_{\text{A2M}}=x_{\text{M}}-x_{\text{A2}}\) is the distance from phase A\({}_{2}\) to point M;
5. \(x_{\text{B2M}}=x_{\text{M}}-x_{\text{B2}}\) is the distance from phase B\({}_{2}\) to point M;
6. \(x_{\text{C2M}}=x_{\text{M}}-x_{\text{C2}}\) is the distance from phase C\({}_{2}\) to point M.  
The conductors' phase reflections A\({}_{1}^{*}\), B\({}_{1}^{*}\), C\({}_{1}^{*}\), A\({}_{2}^{*}\), B\({}_{2}^{*}\), C\({}_{2}^{*}\) are situated at the same distances in the direction of the \(x\) axis. Figure 2 shows that magnetic field strength vector \(H_{in}\) is distributed into two vectors as follows: vector \(H_{iny}\), which varies following the law of sines; and vector \(H_{inx}\), which varies following the law of cosines. The magnetic field strength reflection vector \(H_{in}^{*}\) is distributed analogically.