Summing over indices using symsum

I am trying to calculate electric field at position due to charges

, at positions .

The equation is .

If I can figure out how to for example just get this sum , I would be able to figure out the equation for the electric field. I tried

u=symunit;
syms k

e0=8.854E-12*(u.s)^4*(u.A)^2/((u.kg)*(u.m)^3);

Q1=10E-9*(u.C);
Q2=15-9*(u.C);
Q3=7E-9*(u.C);

r1=[1 4 2]*1E-3*(u.m);
r2=[-2 0 5]*1E-3*(u.m);
r3=[-1 -2 3]*1E-3*(u.m);

r=[5 5 5]*1E-3*(u.m);

Q=symsum(Qk,k,1,3)

Unrecognized function or variable 'Qk'.

That obviously didn't work. Is there a way to make it work with 'symsum'?

[Torsten]

Why do you use symbolic variables if all variables involved have numeric values ?

[RH]

Probably because I did not know what else to use. Any suggestions?

[Walter Roberson]

u=symunit;
syms k
e0 = sym(8854)*sym(10)^(-15)*(u.s)^4*(u.A)^2/((u.kg)*(u.m)^3);
Q1 = sym(10)*sym(10)^(-9)*(u.C);
Q2 = sym(15)*sym(10)^(-9)*(u.C);
Q3 = sym(7)*sym(10)^(-9)*(u.C);
r1=[1 4 2]*sym(10)^(-3)*(u.m);
r2=[-2 0 5]*sym(10)^(-3)*(u.m);
r3=[-1 -2 3]*sym(10)^(-3)*(u.m);
r=[5 5 5]*sym(10)^(-3)*(u.m);
Qs = [Q1, Q2, Q3];
Q = sum(Qs)

Q = 

[Walter Roberson]

If you have somehow created a list of numbered variables that is too long to make it practical to put them into a list by name, then what you should do is...

Not create a list of numbered variables that is too long to make it practical to put them into a list by name.

[Dyuman Joshi]

Note that the sum isn't just over Q, but rk as well

(Without syms and symunit but values according SI units)

e0=8.854E-12;
Q=[10E-9 15E-9 7E-9];
R=[1 4 2;-2 0 5;-1 -2 3]*1E-3;
r=[5 5 5]*1E-3;
r0=vecnorm(r-R,2,2).^3;
out=sum(Q.*(r-R)./(4*pi*e0*r0),1)

out = 1×3

1.0e+06 * 4.3424 3.1998 1.5735

Answer 1

[Torsten]

u=symunit;
Q(1)=10E-9*(u.C);
Q(2)=15E-9*(u.C);
Q(3)=7E-9*(u.C);
Qsum = sum(Q)

Qsum = 

[Torsten]

u=symunit;
e0=8.854E-12*(u.s)^4*(u.A)^2/((u.kg)*(u.m)^3);
Q(1)=10E-9*(u.C);
Q(2)=15E-9*(u.C);
Q(3)=7E-9*(u.C);
rk(1,:)=[1 4 2]*1E-3*(u.m);
rk(2,:)=[-2 0 5]*1E-3*(u.m);
rk(3,:)=[-1 -2 3]*1E-3*(u.m);
r=[5 5 5]*1E-3*(u.m);
Qsum = zeros(1,3);
for k = 1:3
   Qsum = Qsum + Q(k)*(r-rk(k,:))/(norm(r-rk(k,:)))^3;
end
Qsum = Qsum/(4*pi*e0);
simplify(Qsum.')

ans = 

Data = separateUnits(Qsum.');
double(Data)

ans = 3×1

1.0e+06 * 4.6438 2.2614 2.1837

Answer 2

[Walter Roberson]

You cannot use a symbolic variable as an index.

I think it is unlikely that it will ever be supported to use symbolic variables as indices.

Create the definite values and sum() the definite values.