UPDATE: I have found a user made function that takes a 3d matrix and visualizes it. Which solved my problem instantly. The function is vis3d if anyone wants to take glimpse.
How to plot a 3D vector field
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Ege Keskin
el 31 de En. de 2019
Comentada: prachi jain
el 20 de Jun. de 2019
Hello. I am trying to plot the magnetic flux density of a permanent magnet around its viscinity. the magnetic flux density at any point in space (x,y,z) has 3 components, Bx,By and Bz, where all of them are functions of x,y and z. My duty is to plot these vector fields. I have the equations written down but I couldn't gain any progress on plotting. In the end, the vector field should look like the iconic magnetic field lines of a magnet. Here is the code and the equations. Thanks for your help.
syms x y z
a = 1; %dimensions of the permanent magnet
b = 1;
c = 0.5;
Nu0 = 1.25e-6; %(m.kg)/(s^2.A^2) permeability of free space
M = 1; %tesla
F_1xyz = atan(((x+a)*(y+b)) / ((z+c)*sqrt((x+a)^2+(y+b)^2+(z+c)^2))); %F1(x,y,z)
F_1xxyz = atan(((-x+a)*(y+b)) / ((z+c)*sqrt((-x+a)^2+(y+b)^2+(z+c)^2))); %F1(-x,y,z)
F_1xxyzz = atan(((-x+a)*(y+b)) / ((-z+c)*sqrt((-x+a)^2+(y+b)^2+(-z+c)^2))); %F1(-x,y,-z)
F_1xxyyz = atan(((-x+a)*(-y+b)) / ((z+c)*sqrt((-x+a)^2+(-y+b)^2+(z+c)^2))); %F1(-x,-y,z)
F_1xxyyzz = atan(((-x+a)*(-y+b)) / ((-z+c)*sqrt((-x+a)^2+(-y+b)^2+(-z+c)^2))); %F1(-x,-y,-z)
F_1xyzz = atan(((x+a)*(y+b)) / ((-z+c)*sqrt((x+a)^2+(y+b)^2+(-z+c)^2))); %F1(x,y,-z)
F_1xyyz = atan(((x+a)*(-y+b)) / ((z+c)*sqrt((x+a)^2+(-y+b)^2+(z+c)^2))); %F1(x,-y,z)
F_1xyyzz = atan(((x+a)*(-y+b)) / ((-z+c)*sqrt((x+a)^2+(-y+b)^2+(-z+c)^2))); %F1(x,-y,-z)
F_2xyz = (sqrt((x+a)^2+(y-b)^2+(z+c)^2)+b-y) / (sqrt((x+a)^2+(y+b)^2+(z+c)^2)-b-y); %F2(x,y,z)
F_2xxyzz = (sqrt((-x+a)^2+(y-b)^2+(-z+c)^2)+b-y) / (sqrt((-x+a)^2+(y+b)^2+(-z+c)^2)-b-y);%F2(-x,y,-z)
F_2xyzz = (sqrt((x+a)^2+(y-b)^2+(-z+c)^2)+b-y) / (sqrt((x+a)^2+(y+b)^2+(-z+c)^2)-b-y); %F2(x,y,-z)
F_2xxyz = (sqrt((-x+a)^2+(y-b)^2+(z+c)^2)+b-y) / (sqrt((-x+a)^2+(y+b)^2+(z+c)^2)-b-y); %F2(-x,y,z)
F_2yyxzz = (sqrt((-y+a)^2+(x-b)^2+(-z+c)^2)+b-x) / (sqrt((-y+a)^2+(x+b)^2+(-z+c)^2)-b-x); %F2(-y,x,-z)
F_2yxz = (sqrt((y+a)^2+(x-b)^2+(z+c)^2)+b-x) / (sqrt((y+a)^2+(x+b)^2+(z+c)^2)-b-x); %F2(y,x,z)
F_2yxzz = (sqrt((y+a)^2+(x-b)^2+(-z+c)^2)+b-x) / (sqrt((y+a)^2+(x+b)^2+(-z+c)^2)-b-x); %F2(y,x,-z)
F_2yyxz = (sqrt((-y+a)^2+(x-b)^2+(z+c)^2)+b-x) / (sqrt((-y+a)^2+(x+b)^2+(z+c)^2)-b-x); %F2(-y,x,z)
Bx = ((Nu0*M)/(4*pi))*log((F_2xxyzz*F_2xyz)/(F_2xyzz*F_2xxyz)); %x component of the magnetic flux density vector at point (x,y,z)
By = ((Nu0*M)/(4*pi))*log((F_2yyxzz*F_2yxz)/(F_2yxzz*F_2yyxz)); %y component of the magnetic flux density vector at point (x,y,z)
Bz = -((Nu0*M)/(4*pi))*(F_1xxyz + F_1xxyzz + F_1xxyyz + F_1xxyyzz + F_1xyz + F_1xyzz + F_1xyyz + F_1xyyzz ); %z component of the magnetic flux density vector at point (x,y,z)
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Respuesta aceptada
Ege Keskin
el 3 de Feb. de 2019
3 comentarios
prachi jain
el 20 de Jun. de 2019
Hello Kenneth,
Did you find the answer to your question?
I am doing a similar thing for my research. Please share if you were successful.
-Prachi
Más respuestas (2)
KSSV
el 31 de En. de 2019
YOu need to define the values of (x,y,z) sibstiutue these values in Bx, By Bz using subs and then use quiver3.
3 comentarios
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