# Quantifying the magnetic force on a magnet moving through a coil?

• I
• rayjbryant
In summary, Raymond Bryanth calculated the terminal velocity of a magnet as a function of the permeability of the surrounding medium and the number of turns of the coil. He found that the velocity decreases as the permeability increases and that the velocity is very small when compared to the speed of the magnet in free space.f

#### rayjbryant

So I'm familiar with the magnet falling through a copper tube demonstration that shows the induced magnetic fields slowing the magnet down.

I know that this experiment is also possible with a conducting coil as long as the coil forms a closed circuit. I'm trying to find a way to calculate the force acting on the magnet as a function of velocity. Does anyone have a paper they can point me toward?

Thank you,
Raymond Bryant

Hello vanhees, I've looked at this paper before.

Something I tried to do was treat each wrap of the coil as an individual segment and integrate to get its contribution. I wasn't sure if my results were reasonable. I get a very small terminal velocity.

coil approximation:
clc
clear all
close all

% magnet dimensions [m]

d = .0127; %magnet height

%mass of magnet [kg]

m_w = .0017;

% other constants

u_0 = 1.26E-6; % permeability of free space constant T m/A
g = 9.81; % gravitational constant m/s^2

%coil properties [m]

w = .000635; %width of wire
N = 100; % number of turns
c = pi*a*2; %circumference
wl = c*N; %wire length
cs = pi*(w/2)^2; %cross sectional area
rho = 1.7e-8; % resistivity of copper [ohm/m]
wr = (rho*wl)/cs; % resistance in wire [ohm]
lt = 0.3048; % length of tube

%magnetic properties

sm = 72730000; % magnetic surface charge density [Mx/m^2]

qm = pi*sm*r^2; % total charge Mx

eff_dist = .003175; %effective distance of magnet [m]

%terminal velocity calculation

p = qm*d;
x = d/a;
val = scalingfunction(x);

v = (8*pi*m_w*g*rho*a^2)/(u_0^2*qm^2*w*val); %terminal velocity calculation

%for one ring

flux = [];
z = 0:.00001:eff_dist;

for i = 1:1:length(z) %z varies from zero to effective distance of magnet

flux(end+1) = (u_0*qm*.5)*(((z(i)+d)/sqrt((z(i)+d)^2+a^2))-(z(i)/sqrt(z(i)^2+a^2)));

end

Total_flux = 2*sum(flux);

delta_t = (2*eff_dist)/v;

emf = (N*Total_flux)/delta_t;

function [val] = scalingfunction(x)
fun = @(x,y) ((1./(y.^2+1).^(3/2))-(1./((y+x).^2 + 1)).^(3/2)).^2;
val = integral(@(y) fun(x,y),-Inf,Inf);
end

#### Attachments

• writeup_short.pdf
276.4 KB · Views: 58
You will not get much in the way of quantitative results.
Trying to analyze one coil turn at a time is hopeless. Just calculating the flux in a 1-turn coil with given current is beyond any introductory physics course.

You'd have better luck with a long solenoid in which case the two
situations (solenoid & tube) are equivalent. You'd have to know the mag moment of your magnet, for openers.

Delta2
Try to contact @kuruman , he has written a mini treatise on this problem , its not my intellectual property so I am not sure I am entitled to give it.

vanhees71