# Measuring Magnetic Moment

Magnets generate magnetic fields that increase in strength as you get closer to the source and decrease in strength as you get further away. By recording the magnitude of the magnetic field using a magnetometer and the distance from the source at different points, we can graph the magnetic field perpendicular to the dipole.

## The approach

For measuring the magnetic moment, we took a giant page of poster board, taped the magnetorquer to the centre of the page and measured out equally spaced intervals from the centre outwards.

To prepare the sensor, the magnetometer was taped to the end of a wooden rod for keeping the sensor in the exact same position at every interval.

Once we were ready, the current was set to the ideal value and magnetic field was recorded from 2cm to 25cm away from the magnetorquer.

## Data

When we simply plot the Magnitude of the magnetic field vs. Distance, we get a non-linear relationship that looks something like this:

This graph is a bit difficult to work out the magnetic moment, so we should linearize the graph.

The formula to calculate the magnetic field at a point is below, where mu_nought is the magnetic constant, r is the distance and the magnetic moment is mu.

$B_{d} = \frac{\mu_0}{4\pi}\frac{2\mu}{r^3}$

$B_{d} = (\frac{2\mu_0\mu}{4\pi})\frac{1}{r^3}$

From this equation, we can see we can approximately linearize the graph by taking the inverse cube of the distance, which we get here:

The best fit line is already calculated and displayed on the graph. From the equation listed above, we can see 2mu_nought*mu/(4*pi) is the slope, so to isolate the magnetic moment, we multiply the slope from the best fit line by 4*pi/(2*mu_nought), which simply leaves the magnetic moment.

For our magnetorquer, the actual magnetic moment works out to be 0.05Am^2

From our magnetorquer design calculation we know our goal magnetic moment is 0.1973Nm/T. Our mesaured magnetic moment is nowhere near our calculated magnetic moment, so we will need to revisit our approach for the fabrication.

To view the data yourself, check the file here.