Magnetic Fields OVERVIEW: This lab gives you the opportunity to map and measure magnetic fields. You will measure Earth’s magnetic field and you will make measurements regarding the magnetic force on a current carrying wire. PHYSICS CONCEPTS: Magnetic field Vector addition Force on a current carrying wire due to a magnetic field NEW SKILLS: Using a compass EQUIPMENT: Compass Magnaprobe (a 3 dimensional compass) Large horseshoe magnet Bar magnet #16 gauge wire loop mounted in frame Solenoid Power supply Ammeter or digital multimeter Ruler Protractor Scale

Background

Magnetic forces are relatively familiar to us. We see them used to guide our way when using a compass, to store information on computer disks, to attach graded lab reports to the refrigerator, and even to manipulate and visualize the nuclei of atoms. Yet, despite all that we do with magnets, the source of magnetism is not always obvious. In this lab you will study several different sources of magnetism and actually measure them.

There are a few things you should constantly be aware of while doing this lab. First, because you have several magnets on your lab table (a compass, a Magnaprobe, a bar magnet, and a large horseshoe magnet), you need to be careful that they are not interfering with one another. The compass will be easily misdirected when the Magnaprobe is nearby, and vice-a-versa. Somewhat more importantly, please keep all magnets away from the computers and monitors. Standard CRT monitors can easily be damaged by large magnets, and the disks in and out of a computer can be erased with these same magnets. Finally, the large magnets will attract each other or certain metals in an almost violent fashion, and they could easily smash fingers if you are careless.

Part I: Detecting magnetic fields

First, you need to play with the compass and the Magnaprobe. What do they do? Each of these is a small bar magnet with a “north” and “south” side. Away from any other magnets, where do these point? What does the Magnaprobe tell you that the compass does not? Be sure that everyone in your lab group has an opportunity to play with these devices.

When you are satisfied that you know every detail of how a compass and Magnaprobe work, you will use the Magnaprobe to “map” the magnetic fields of at least three different magnetic field producers, including:

1. a bar magnet

2. a line of current at the bottom of the current carrying loop

3. a current carrying solenoid

Both the current carrying loop and solenoid can be supplied current with the power supply and appropriate cables. (At this point you’ve probably connect enough circuits that this will be a straightforward process. If it isn’t, make sure that you consult your instructor or lab aide.) In both cases, make sure that:

1. You have an ammeter (or DMM measuring current) connected appropriately in series with your wire/solenoid. The meter should be set so that it can measure up to 1.0 Amp.

2. The current does NOT ever exceed 1.0 Amp. In most cases you can use much less than this.

3. You only have the current flowing for a few seconds at a time. Make sure that you disconnect the circuit or turn off the power supply so that the wires or other components do not get too hot.

Given these guidelines, again play with the magnetic fields. Use the Magnaprobe to see the intensity and direction of a magnetic field as it approaches a bar magnet, as it goes around a line of current (at the bottom of the current carrying loop), and when it is inside of a current carrying solenoid. Make sure that everyone has the chance to use the Magnaprobe, and answer the questions in this part of the Report.

Part II: Measuring Earth’s magnetic field

The planet’s magnetic field is one of those wondrous things that we often take for granted. It should be clear from playing with the compass and the Magnaprobe that there is some inherent magnetic force that just “is”. This magnetic field is produced deep inside Earth, interacting with things ranging from your compass needle to storms of charged particles coming from the Sun.

You can measure the magnitude and direction of the Earth’s magnetic field relatively easily. In fact, you should first simply hold the Magnaprobe away from other magnetic sources and observe which direction it points, noting that it doesn’t simply point “north” or “south,” but in a vertical direction as well.

To get a quantitative measurement for Earth’s magnetic field, all you have to do is create another magnetic field to “fight” with Earth’s magnetic field until the two fields cancel one another. If you know the magnitude and direction of the magnetic fie ld that you produced, then you also know the magnitude and direction of the Earth’s field. You will use this strategy to measure both the vertical and horizontal components of Earth’s magnetic field, and use these to find Earth’s total magnetic field.

First, you will use the compass and the solenoid (connected to the power supply as in the previous part) to determine the horizontal component of Earth’s magnetic field. With no other magnetic forces nearby, find the direction that your compass needle naturally points. The compass shows you this direction, but it doesn’t show you how strong the field is. If you produce a known magnetic field that is perpendicular to Earth’s such that the compass turns 45° (so that it is positioned exactly halfway between the pull of

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Earth’s magnetism and another known magnetism), then you will know that you have produced a magnetic field that is equal in magnitude to the horizontal component of Earth’s field.

Figure 1: A compass in a horizontally oriented solenoid

So, how are you going to do this? You should have found that you can produce a fairly uniform magnetic field inside of the solenoid. With the solenoid disconnected, place the compass inside of it. (See figure 1.) Position the solenoid so that, when you do put current through it, its magnetic field will be perpendicular to the direction that the compass needle naturally points. Then, you can connect the solenoid to the power supply and increase the current until the compass needle is deflected so that it is exactly in between the two external fields.

The magnitude of the magnetic field (in units of tesla) you have just produced is:

B = µonI (1)

where µo is the “permeability of free space” (4π ×10−7T-m/A), n is the turns per unit length of the coil in m−1, and I is the current in amperes (A). The measurement of current is read easily enough from your ammeter. The number of turns (coils) per unit length is simply calculated by counting the number of turns in your solenoid and dividing by the solenoid’s length.

Using this information, determine the strength of the horizontal component of Earth’s magnetic field at your location. Show your work and answer in this section of the Report.

Next, you want to determine the vertical component of the Earth’s magnetic field. The Magnaprobe should show you that the planet’s field doesn’t just point northward, but also down into the ground. To measure the size of this component of the magnetic field, you simply need to cancel it out with an opposing field, in a similar fashion to what you did with the horizontal component. In this case, you should orient the solenoid vertically and run current through it so that it produces a magnetic field that points upward, opposite of the field the Earth produces. (See figure 2.) Once there is a great enough field produced by the solenoid that it cancels out the Earth’s field, a Magnaprobe inside the solenoid will lie flat, parallel to the ground. (Note that the Magnaprobe magnet can sometimes stick, so you should tap its handle occasionally to make sure it is rotating freely.)

Figure 2: A Magnaprobe is held inside a vertically oriented solenoid.

Conduct this experiment and calculate the vertical component of the Earth’s field and show your work in the Report. Once you’ve done this, you can calculate the total magnetic field inherent to your location. Answer the rest of the question in this part of the Report as well.

Part III: The magnetic force on a current carrying wire

As shown in figure 3, you can place a loop of current carrying wire inside the magnetic field produced by the horseshoe magnet. If you haven’t already, you will probably solve lots of problems from the text in which you calculate how much force is produced when a magnetic field interacts with moving charges. In the first part of this lab, you looked at the magnetic field produced by these moving charges, but in this part of the lab you will see how these moving charges are affected by an external magnetic field.

First, set up a line of current so that it is directed perpendicular to the magnetic field produced by the horseshoe magnet, as shown in figure 3. You can verify the direction of the magnetic field produced by the horseshoe magnet by using your Magnaprobe, but be careful not to let the delicate Magnaprobe get pulled into the strong horseshoe magnet, since the precision bearings of this instrument could be damaged. Play with this setup by supplying current to the wire. Vary the amount of current, the direction of the current, and the orientation of the magnet and answer the first question in this part of the Report. You should be getting the loop of wire to swing into or out of the horseshoe magnet. If not, check with your instructor to make sure that everything is set up correctly; and at all times make sure that the current is less than 1.0 amp and that it is not left on for very long. (If any part of the wire or resistors connect to the wire begin to get hot, you are leaving the current on too long!)

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Figure 3: A magnet is positioned so that its field is perpendicular to a line of current.

You should be noticing that the greater the current in the wire, the greater the magnetic force (as demonstrated by the loop of wire getting pushed one way or another). Being a naturally inquisitive person as well as a data desiring scientist, you are probably wondering what else you can do to really show this relationship. This is a measurement that you will need to estimate somewhat.

Consider that the force perpendicular to a current carrying wire is:

F I B= l (2)

assuming that the average magnetic field (B) and the current (I) are perpendicular to one another, as they are in this particular setup. The length of wire, l, is the length of wire that is in the magnetic field (not necessarily the entire length of the wire). The total force will be the product of this force and the nuber of turns.

The torque about the pivot point of this loop caused by the force due to the magnetic field is simply the product of the lever arm and the force, or:

nI Baτ = l (3)

where a is the vertical dimension of the loop (the distance between the top and bottom) and assuming that the current in the wire and the magnetic field are always approximately perpendicular to one another. (In this case, this turns out to be a valid assumption, due to the curving of the magnetic field lines as the wire moves away from the strongest part of the horseshoe magnet.) This expression shows why the loop is made to swing in or out, but it doesn’t describe the torque in the opposite direction, balancing the torque due to magnetism. That torque is due to gravity, trying to swing the loop back to its original position.

The torque due to gravity must be due to the weight of different parts of the loop and the distance of the center of mass of the loop from the pivot You can show that the torque due to gravity is:

τ = mga2

sin θ (4)

where θ is the angle that the loop is away from vertical.

You will use equations 3 and 4 to estimate the average magnetic field of the horseshoe magnet.

Report: Magnetic Fields

Name: ________________________________ Partners:_______________________________ _________________________________ _________________________________ Lab Station: ___________________________ Date: _________________________________

Part I: Mapping magnetic fields

QUESTION: What does the magnetic field produced by a bar magnet look like? Be as descriptive as possible, and include a drawing..

QUESTION: What does the magnetic field produced by a line of current look like? Be as descriptive as possible, using a drawing as necessary. (Hint: To aid drawing such a magnetic field, represent the wire as a dot such that the current would be coming out of the page.) Show the relationship between the directions of the current and the magnetic field lines. How does the magnitude of the field due to the line of current compare to that of the bar magnet? How can you tell?

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QUESTION: What does the magnetic field produced by a current carrying solenoid look like? Be as descriptive as possible, using a drawing as necessary. Show the relationship between the direction of the current in the solenoid and the direction of the magnetic field inside the solenoid. How does the magnitude of this field compare to the other two?

Part II: Measuring Earth’s magnetic field

QUESTION: In what direction does the Earth’s magnetic field point, based on your observation of the Magnaprobe? Note both the horizontal and vertical components of this vector. QUESTION: What is the magnitude of the horizontal (parallel to the ground) component of Earth’s magnetic field at your location? Show your answer and all of your work, including a sketch of the compass needle (oriented at 45° from magnetic north) and the forces acting on it.

QUESTION: What is the vertical component of the Earth’s magnetic field at your location? Show all of your work and your answer clearly. QUESTION: What is the total magnetic field produced by Earth at your location? Compute this by summing the two vector components calculated above. Remember that this magnetic field is a vector; so describe the magnitude and direction of this total magnetic field. (The direction you calculate should correspond fairly well to the natural direction that the Magnaprobe magnet points when exposed only to Earth’s magnetic field.) Does the direction you obtain agree with the direction you get from the isolated Magnaprobe?

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QUESTION: Why does the planet’s magnetic field point into the ground? Sketch the Earth and the magnetic field surrounding it to explain your answer. QUESTION: If the planet’s magnetic field were produced by some kind of loop of current deep at the Earth’s center, how would this loop be oriented (i.e., what direction would it be pointing) and what direction would the current be flowing? (Note: Although there isn’t a physical loop of wire at the center of the planet, this is a good model of how charged particles flow in the liquid portion of Earth’s core.)

Part III: The magnetic force on a current carrying wire

QUESTION: If the wire is pushed out of the magnet, what direction must the current and magnetic field be pointing relative to one another? (There are two answers to this question, and they should correspond to one of the “right hand rules” in your text.) Use a sketch to clarify you answer, if necessary.

QUESTION: What is the average magnetic field of your horseshoe magnet? Show your work, using the equation derived above. Estimate your uncertainty in this measurement. Are there any systematic errors which could affect the accuracy of the measurement?