# Calculating the terminal velocity of a magnet falling through a copper coil

• rayjbryant
In summary, the conversation discusses the calculation of terminal velocity for a magnet falling through a copper coil. The dimensions, mass, and magnetic properties of the magnet and coil are taken into consideration, as well as the use of a scaling function. The purpose of this calculation is to determine the necessary specifications for a model that will work effectively in a desired commercial application. The possibility of experimental error is also mentioned.
rayjbryant
The magnet being used

The main body code.:
% magnet dimensions [m]

d = .0127;
r = .00238;

%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 in/s^2

%coil properties [22 gauge wire] [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; %

eff_dist = .003175;

%terminal velocity

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);

The scaling function code.:
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

terminal velocity ends up being: 1E-4 m/s

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rayjbryant said:
I'm attempting to calculate the terminal velocity of a magnet falling through a copper coil by assuming there are enough turns to treat it as a copper tube.
How is your coil terminated? Are the ends connected together? How are eddy currents going to form in a coil to generate a retarding force?

When you use a copper tube in your simulation, do you get the expected result?

Yes, the ends are connected to allow current to flow and eddy currents to form. The desired effect was achieved with a physical model using a weaker magnet and 20 gauge coil but not enough damping or current flow occured. The purpose of this code is to find a combination of magnet strength, wire size, and turn number to build a model that will work to desired specifications. After which a cost analysis will be performed to see if the system is economically feasible to use in the desired commercial application.

berkeman
And sorry I misread the first part of your post. The equation used in the code to calculate the terminal velocity automatically assumes the apparatus is a solid tube. I've performed several copper tube and magnet experiments as well as observed quite a few, and none have a terminal velocity as low as 1E-4 m/s. If any error does occur, it should be an experimental terminal velocity higher than the computer model, since copper coils are not as effective at damping as copper tubes.

Last edited:
Keith_McClary

## 1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water, due to the balance of gravitational force and air resistance.

## 2. How is terminal velocity calculated?

Terminal velocity can be calculated using the formula: Vt = √(2mg/ρAC), where Vt is the terminal velocity, m is the mass of the falling object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient.

## 3. What factors affect the terminal velocity of a falling object?

The terminal velocity of a falling object is affected by the mass, size and shape of the object, the density of the fluid, and the presence of any external forces, such as wind.

## 4. How does a copper coil affect the terminal velocity of a falling magnet?

The copper coil creates a magnetic field that exerts a force on the falling magnet, causing it to experience a resistive force in addition to air resistance. This results in a slower terminal velocity for the magnet compared to if it were falling through air alone.

## 5. Why is calculating the terminal velocity of a falling magnet through a copper coil important?

Calculating the terminal velocity of a falling magnet through a copper coil can help us understand the principles of electromagnetism and the effects of external forces on falling objects. It can also be useful in designing and optimizing systems that use magnets and coils, such as generators and motors.

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