Activity 22 – Magnetic Field of a Bar Magnet
Studio Physics I
In this activity we will study the magnetic field created by a bar magnet, both theoretically
and experimentally. Although, to date, no isolated magnetic monopoles have ever been
discovered, we will see how well we can model a bar magnet as two magnetic monopoles,
one at each end of the magnet. This will enable us to calculate the magnetic field using the
same method we used to find the electric field created by two charges, one + and one –.
1. Using a compass, explore and sketch the magnetic field around your bar magnet.
Remember that the compass needle will align with the direction of the field. Does the pattern
you get resemble the electric field around a pair of equal +/– charges (a “dipole”)?
The magnetic force and the electric force are NOT the same force. The electric field
and magnetic field are NOT the same field. Nevertheless, we will explore in what ways
the magnetic field due to a bar magnet (which you mapped out in #1) is similar to the
electric field produced by an electric dipole.
2. The figure below (left) shows your bar magnet and its dimensions as seen from above
looking down at the magnet resting on your table. Measure and record L and W.
S
-
N W
+
L
3. We will now analyze the bar magnet with the simplest possible magnetic field model
consisting of one positive magnetic charge (monopole) and one negative magnetic charge, as
shown above (right). Note that the fictitious magnetic charges are both well inside the
boundary of the magnet. Since we can only measure the magnetic field outside the magnet,
we do not worry about what our model would predict inside the boundary of the magnet.
This is typical for many types of numerical models in electromagnetic analysis.
Experience has shown that a good place for the charges in this simple model is W/2 from the
respective ends of the magnet, along the centerline. To make the analysis simpler, we select
an X,Y coordinate system that represents the symmetries of the bar magnet, as shown below:
Y
-
+
(W/2-L/2,0)
(L/2-W/2,0)
X
Define D = L/2–W/2, then calculate D using the values you measured for L and W.
© 2004 Bedrosian, Rev. 10-Apr-05 GB
4. The next step is to develop a formula that predicts what the magnetic field will be at any
point on the X axis at coordinate (x,0), where x is measured from the center of the magnet.
Assume that the magnetic field created by a magnetic charge should obey a similar formula
to the electric field from an electric charge, where Qm is the magnetic charge. The formula
for the magnetic field (B) along the X axis is

1  Qm
1  Qm
Q  1
1
Bx 

 m

2
2
2
2
4  x  D 4  (x  D)
4   x  D (x  D) 
where Qm is for your bar magnet. What is the direction of the magnetic field vector at
locations on the X axis to the right of the + charge (north pole)? (Explain using what we
know about the magnetic field near a north pole.) Explain where this equation came from.
5. The equation in step 4 is our prediction of how the magnetic field will change with
location as we move along the X axis. In order to check this, we need to measure the
magnetic field at a number of points. Before you take the measurements, you should become
familiar with the equipment we will use to measure the magnetic field, known as a Hall
probe. (You can read about the Hall Effect in your book in Section 28-5.)
Set up your Hall probe as explained on the attached sheet. Make sure to note which direction
of the magnetic field vector is measured by the Hall probe. Get the file Magnet.xmbl from
the course web site Activities page or from your Studio Physics CD in the Physics 1 folder
and open it in LoggerPro. You can read the magnetic field values in real time on the screen
without needing to click on the “Collect” button. Experiment with using the probe. You will
notice that even when the probe is held away from obvious sources of magnetic fields, such
as your bar magnets, you see a non-zero reading. From the behavior of the probe
measurements, determine if this is caused by a real magnetic field or is an electronics artifact
or both. You can zero the probe using Logger Pro by clicking on the LabPro picture and then
on the picture of the probe. You will need to zero the probe to get the most accurate data.
6. Measure 8 points of magnetic field along the X axis. The points should be at the
following locations measured from the center point of the magnet: 6.5, 7.0, 7.5, 8.0, 8.5, 9.0,
9.5, and 10.0 cm. Record the data on your write-up. You should get values in the range of
10-50 gauss at 6.5 cm and 1-10 gauss at 10 cm. Make a graph – with numbers and to scale,
not just a sketch – of magnetic field versus x.
7. Download the Excel spreadsheet Magnet.xls from the course web site. Enter the values of
L and W in cm, and the magnetic field in gauss, into the appropriate cells. The spreadsheet
will calculate a value for Qm/(4 ) so that the predicted value of Bx from the formula matches
the value you measured for the first (closest) point. It uses this value to calculate the
predicted values of Bx for all points. Plot the predictions on the same graph as your
measurements. Discuss how well the points matched – or not – in terms of both the absolute
differences between the measured and predicted values, and % differences. If you took the
measurements carefully, you should have matched the predictions within 10% or less.
8. Based on your exploration of the magnetic field lines in step 1 and the comparison of the
measured and predicted values in step 7, would you conclude that the magnetic field from a
bar magnet behaves like the electric field from two opposite charges? Explain your answer,
don’t just say yes or no, both qualitative (overall behavior) and quantitative (numerical).
© 2004 Bedrosian, Rev. 10-Apr-05 GB
THE MAGNETIC FIELD SENSOR (HALL PROBE)
To measure magnetic field strength, you will need a measurement probe (the magnetic field
sensor) and an interface to the computer. Each of these components is described below.
Magnetic Field Sensor
The magnetic field sensor is composed of the wand, the amplifier, and the LabPro data
acquisition device. These parts are sketched below.
Wand
Amplifier
Box
Adapter Plug
Analog Input Port 1
LabPro
The Wand is a hollow plastic tube with a Hall effect transducer chip at one end (shown
above as the circle on the right hand end of the wand). The chip produces a voltage that is
linear with the magnetic field. The maximum output of the chip occurs when the area vector
of the white dot on the sensor points directly toward a magnetic south pole, as shown below:
© 2004 Bedrosian, Rev. 10-Apr-05 GB
The Amplifier is contained in a small box and allows you to measure a greater range of
magnetic field strengths. The switch on the box is used to select the desired amplification.
The low amplification setting is used to measure medium strength magnetic fields. The
range of the sensor in low mode is about ±50 gauss. The sensor is unreliable when
measuring values of magnetic field higher than about 50 gauss. Unless otherwise
instructed, always use the low setting. The high amplification setting is used to measure
weak fields. The range of the sensor in high mode is around ±2.5 gauss. The actual range
will vary from one magnetic field sensor to another. Note: 1 tesla = 10 4 gauss; the magnetic
field of the earth is approximately a quarter to half a gauss.
The LabPro allows the computer to communicate with the wand. In order to measure
magnetic fields, the wire leading out of the amplifier box should be plugged into the LabPro
analog port 1 via an adapter plug. The LabPro itself should be plugged into the USB port of
the computer after the LoggerPro-3 software has been loaded. A file called Magnet.xmbl
(available on the Studio Physics CD in the Physics I folder) should be opened in LoggerPro-3
to begin taking measurements.
The amplifier setting should be on low to measure fields due to bar magnets.
© 2004 Bedrosian, Rev. 10-Apr-05 GB