trajectory of an electron in an electron beam evaporator

Question

Ingrid Morales Flores 2023-6-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1984849-trajectory-of-an-electron-in-an-electron-beam-evaporator

回答： Swapnil Tatiya 2023-7-13

I already made a code, but I want the path to be circular, please help

clc; clear all

M = 100 ;

t = linspace(0,20,M) ;

m=9.1e-31 ;

q=-1.6e-19 ;

P = zeros(M,3) ;

V = zeros(M,3) ;

p = rand(1,3) ;

v = rand(1,3) ;

P(1,:) = p ;

V(1,:) = v ;

c = rand ;

E=[0 0 c] ;

d = rand ;

B=[0 0 d] ;

for i = 2:M

f=q*E+q*cross(v,B) ;

a=f/m ;

v = v+a*t(i) ;

p = p+v*t(i) ;

P(i,:) = p ;

V(i,:) = v ;

end

plot3(P(:,1),P(:,2),P(:,3));

axis equal

xlabel('x'); ylabel('y'); zlabel('z');

grid on

set(gca,'fontsize',14);

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Answer 1

Swapnil Tatiya 2023-7-13

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Hi @Ingrid Morales Flores,

The electron shall not go in a circle when both E field and B field are applied simultaneously,so I've modified your code such that there's just B field so that you get a trajectory as you desired.

M = 100; 
t = linspace(0,20,M) ; 
m=9.1e-31 ;
q=-1.6e-19 ;
P = zeros(length(t),3) ; 
V = zeros(length(t),3) ;
V(1,:) = [0 rand(1) 0] ;
d = rand(1) ;
B=[0 0 10^-12] ;
for i = 2:length(t)
    f=q.*(cross(V(i-1,:),B));
    a=f/m;
    V(i,:) = V(i-1,:)+a*(t(i)-t(i-1)) ; 
    P(i,:) = P(i-1,:)+V(i-1,:)*(t(i)-t(i-1)) ;
end
plot(P(:,1),P(:,2))
grid on