About your report:  You'll do all your work for this lab on your poster paper.

About working with a partner (or not): You may work with one partner. If you do so , one of you will plot the field on one side of the magnet and the other will plot the the field on the other side of the magnet. Each of you will do Part B on your side of the magnet. Write your name on the side of the magnet that you do. You will then mail one poster for the two of you. If you're working alone, you only have to plot the field on one side of the magnet.

Goal: To investigate natural magnetism and the magnetic field of the Earth by plotting the magnetic field lines around a bar magnet.

Prelab: Assemble your equipment and read section 22.1 of your text as well as the Introduction below.

Equipment:

Poster paper
Bar magnet (about 6 inches long)
Small compass (about 1-cm diameter)
Large, empty cardboard box

Introduction

It's important that you understand how a compass works in order to know how to orient your bar magnet for this experiment.  You probably knew even before reading 22.1 that the needle of a compass is naturally magnetic.  You may not have known that the north magnetic pole of the compass needle points to the Earth's magnetic south pole.  Nevertheless, that makes sense, because opposite magnetic poles attract.

Now here's a coincidence.  The Earth's magnetic south pole isn't too far from the Earth's geographic north pole.  That's why we say compass needles generally point in the direction of geographic north.  In order to simplify terminology, let's use these acronyms:  GN/GS = Earths' geographic north/south poles; MN/MS = Earth's magnetic north/south poles.  In terms of location on the Earth, GN and MS are close to each other (as are GS and MN).  You must have this straight before going on. Therefore, here's Important Point #1 for this lab:

MS is geographically near GN.

We know this statement is contrary to common usage, but common usage is incorrect.  You'll even see MS labeled as MN on maps.  (That's to avoid confusing people who don't know any better.  Hopefully, you're not confused.)

Due the fact that MS is close to GN, compass needles point approximately toward GN in North Carolina and many other parts of the country.  The angular difference between MS and GN is called the declination and is different for different locations.  For North Carolina, the declination is only about a degree.  That's because from our location, MN and GS are almost in a direct line.  Therefore, we won't worry about the difference in this lab.

Here's Important Point #2.  The polarity of a compass needle can be switched by strong magnetic fields.  If your compass has been in the vicinity of a strong magnet, the compass needle's north pole may have been switched to a south pole and the south pole to a north pole.  That means the end of the needle labeled N (or painted a distinguishing color in some cases) may be mislabeled.  You must know how to determine if this is the case.  That brings us to:

Important Point #3.  You must know which direction is geographic north at your current location.  That's the standard from which you start your work in this lab.  By knowing the direction of GN, you can see which end of the compass needle points that way.  That end of the compass needle will be the magnetic north pole of the needle (because it's pointing to MS, right?).  If by chance you have a strong magnet close to where you're working, keep the compass far from it, so that the polarity of the needle doesn't change when you least expect it.

The Last Important Point.  Just as your compass needle can switch polarity, so can your bar magnet.  Just because the bar magnet is labeled N and S on the ends (assuming that it's labeled) doesn't mean those labels are correct.  You have to test them.  How do you do that?  With your compass.  Bring the compass close to one end of the bar magnet.  If the bar magnet attracts the north (or south) pole of the compass needle, then that end of the bar magnet is a south (or north) pole.  If the bar magnet's poles are indeed switched, then label the poles in some way so that you don't inadvertently overlook the switch later.

To review, here's what you need to do to insure that you know which pole is which for the Earth, the compass, and the bar magnet:

1. First, you need to know which direction in your classroom is GN.  Ask your facilitator if you don't know.  Once you know the direction of GN, you also know the direction of MS to within a degree.
2. Knowing the direction of MS, you can check your compass to see which end of the needle is the north pole.
3. Knowing which end of the compass needle is the north pole, you can use it to determine which end of your bar magnet is the north pole.

We expect you to do the above before continuing with the experiment.  By the way, you'll be glad to know that the Earth's magnetic polarity isn't going to switch during your experiment.  However, over the span of thousands of years, the polarity of the Earth has reversed itself.

Part A:  Plotting magnetic field lines using a compass

Use a soft-leaded pencil to write on your poster paper.  Don't use a pen, because you'll want to be able to erase.  Refer to the diagram below for the general setup of your poster paper.

1. Place the cardboard box upside down on the floor in order to form a platform away from the wall and metallic chair and table legs that might exert a magnetic influence.  Lay the poster paper on the box.  Don't lay the bar magnet on the poster paper yet.

2.  You need a small compass for this. (A 1-cm compass has been provided you.) Lay the compass on the poster paper.  Use the compass to determine the direction of the Earth's magnetic south pole (MS). 

3. Orient your poster paper so that one side is parallel to a north-south line.  Near one corner of the paper, draw a 6-cm long arrow pointing in the direction of MS.  Label it MS.  Write your name (or names if you have a partner) beside the arrow.  At this point, don't move the box or the paper until you've completed your field mapping.

4. Place your bar magnet in the center of the poster paper. Orient the magnet so that its long axis is perpendicular to the direction of MS.  Position the magnet so that when you are facing toward MS, the south pole of the bar magnet is on your right.

5. Trace the magnet shape onto the paper and label the positions of the magnet’s N and S poles on the paper.  At this point, don't move the magnet until you've completed the field mapping.

6. Starting near a corner of the N end of the magnet, place 5 tic marks spaced 4 millimeters apart down the long axis of the bar magnet. (See the figure.)  To be more specific:  Place the first tic mark at a corner of the N end.  This will be central tic mark of the five.  Then put two tic marks on either side of the central one.  Note that these instructions are written assuming the bar magnet is about 15 cm long (a typical length).  If your magnet is significantly shorter, you may have to put the tic marks closer together.

7. If you're working with a partner, your partner will do the same thing that you do but on the opposite side of the magnet.  With a partner, you'll be able to map the magnetic field on both sides.  Working alone, you'll just map the field on one side.

8. Now take your compass and place it such that one of the tic marks lies on the circumference of the compass while at the same time the S end of the needle points directly to the tic mark.  With a pencil, make another tic mark on the opposite side of the compass, i.e., at the place to which the N end of the compass needle points.  See Figure 1.  This works best with a small diameter compass.  If you have a large compass, make the best of it.

Figure 1	Figure 2

9. Now move the compass so that the S end of the needle points at the new tic mark you just made.  Again make a new tic mark on the opposite side of the compass, at the place to which the N end of the compass needle points.  (See Figure 2.) Keep repeating this process until the trail of tic marks reaches the edge of the paper or returns to the south end of the magnet.

10. Connect the tic marks with a smooth curve to produce a magnetic field line.   Draw an arrow on the line to indicate the direction of the field.

11. Repeat steps 8-10 for each of the remaining tic marks at the N end of your side of the magnet.  Your partner, if you have one, will do the same thing on the opposite side.

You can remove your poster paper now from the cardboard box. 

Part B:  Interpreting your magnetic field plot

1. In an unused corner of your poster paper, make a drawing of what you would expect the magnetic field of a bar magnet to look like; draw this picture with the same orientation as your original bar magnet.  Label the poles and place arrows on the field lines.  Use your text as a reference as needed.

2. Compare your diagram from the last step with the field lines you plotted using the compass. You should notice a distinct departure from symmetry in your actual field lines.  How can you account for this?  Perhaps you realized that you weren't plotting just the magnetic field of the bar magnet.  The magnetic field of the Earth was superimposed on the bar magnet's field.  While the Earth's field is weaker, it does have an influence.  This is why it was important to orient your bar magnet in a particular way with respect to the Earth's field.  Here’s a way to see if the asymmetry in your field plot makes sense. Construct the perpendicular bisector of the rectangle that represents your bar magnet. (See Figure 3 below.)  Mark a point where this line intersects one of your field lines on either side of the magnet.  (Only one side is shown below, but partners should work on opposite sides of the paper simultaneously.)  Now you know, from symmetry, that the magnetic field from the bar magnet is in the East-West direction at every point on the perpendicular bisector of the bar magnet, while the magnetic field of the Earth is in the North-South direction; therefore, they are perpendicular. Thus, if we know the direction of the net magnetic field, then we can find the ratio of the strength of the bar magnet to the strength of the Earth’s field.

Figure 3	Figure 4

For point P, do the following.  (Use Figure 4 as a guide.)

1. Draw a vector tangent to the field line and about 10 cm long.  This represents the net magnetic field at point P.  (Do you see why?)

2. Usually when you construct a vector sum, you start with the vectors that you're going to add and then find the resultant vector.  In the present case, you have to work backwards.  Given the net field vector = + , construct the vectors that represent the fields of the earth and the bar magnet .  These vectors must be perpendicular, so you really just have to construct a rectangle that has as a diagonal.  Label the three vectors. 

3. Measure the lengths of and and calculate the ratio of the magnitudes of and .  Use this ratio and the known magnetic field of the Earth (look it up) to calculate the magnitude of the magnetic field of the bar magnet at point P in units of Teslas.   Show your work clearly and in large print in an empty portion of your poster paper.

4. Do you expect the value that you calculated for the magnetic field of the bar magnet to change as you move along the perpendicular bisector?  Explain.  Base your explanation on evidence from your field plot and what you know about magnetic forces.  Once again, write in large print in an empty portion of your poster paper. Here's a way to make your answer very clear. Sketch a series of three vector sums at three different distances from the bar magnet along the perpendicular bisector. (Draw these in a corner of your paper. They should represent what you expect to happen.) In your sketches, make it clear which fields you expect to change in magnitude and which you don't expect to change. Write a conclusion based on a comparison of the three sketches.

Submitting your work

Since you can't fax your poster paper without cutting it up, the method of submission for this lab is by mail. You may either use a mailing tube or carefully fold your poster down to about an 8" x 11" size. You can then mail it in a 9" x 12" envelope. Include your field sketches from Part B. Ask your facilitator to help with the mailing.