问题
I want to make a plot force vs position (for coulomb's law) and estimate the constant e0. I have the values of charges , q1=1,q2=1. I have for example the
position=[0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1];
force=[0.08,0.015,0.013,0.0062,0.0016,0.00519,-0.00159,0.00118,...
0.0061,0.00155,0.00143];
Coulomb is F= (1/4*pi*e0) * q1*q2/r^2. So, it is in the form:
y=ax^-m , where a= (q1*q2/4*pi*e0)
I am doing:
p=polyfit(-log10(position),log10(force),1); % I am not sure about '1' and minus
m=p(1);
a=10^(p(2)); % I am not sure about a
xp=0.1:0.1:1.1;
yp=a*xp.^(-m);
plot(position,force,'o',xp,yp)
e0=q1*q2/4*pi*a
I am not finding a right value for e0.Am I doing something wrong? The m value should be -2 but I am taking :
m =
1.6287 - 0.2008i
回答1:
There are a couple of reasons this is wrong. Firstly, you've missed some parentheses out of your definition of Coulomb's law. It should be
F = 1/(4*pi*e0) * q1 * q2 * r^-2
This means that your final calculation of e0 should go like
a = 10^p(2);
e0 = ((q1 * q2) / (4 * pi)) / a;
The other reason this is wrong is that, in fact, the definition of the law is still wrong for your context. You have only positive charges (q1, q2) there, but clearly the force goes negative at some point. Since you're working in log-space to estimate the parameters, this is not going to work as you will get a complex number out. Your definition of Coulomb's law for your data should be
|F| = 1/(4*pi*e0) * |q1 * q2| * r^-2
That is, you only have the absolute values. Therefore you should do the fitting using abs(force) instead of just force.
回答2:
Since a= (q1*q2/4*pi*e0), e0 should be
e0=a/(q1*q2/4*pi)
Check it.
来源：https://stackoverflow.com/questions/16250137/curve-fitting-estimate-parameter-inverse-square-law