GEOG/PHYS 182 Magnetic Field Measurement

Objective: To examine the magnetic field of a permanent bar magnet and an electromagnet.

I. Introduction to Magnetic Field

You have seen that all the forces in the universe can be broken down into four basic categories: gravity, electromagnetism, weak (nuclear), and strong (nuclear). The force of electromagnetism can be thought of as having both electric and magnetic parts. You have studied the electric component of this force in the Electric Field Measurement lab by determining the behavior of the electric field lines between three configurations of pairs of conductors held at different voltages. In today’s lab you will examine the magnetic field in the vicinity of two types of magnets, which are a permanent bar magnet and an electromagnet created by a pair of Helmholtz coils. The electromagnet consists of two identical circular coils of wire that are coaxial (have the same axis) and are separated by a distance equal to the coil radius.

Magnetic fields are produced by moving charges, which are referred to as electric currents. Remember that the electric field can be produced by both moving and stationary charges. Hans Christian Oersted was the first to discover that a compass needle was deflected when placed near a current carrying wire during an electricity demonstration in 1820. For the case of the electromagnet that we will use today, the magnetic field arises from the electrical current passing through the wires of the Helmholtz coils. For the permanent bar magnet, the magnetic field arises from the motion of the electrons circulating around the nuclei of the atoms in the magnet, which is also considered a type of current.

Just like the electric field, the magnetic field is a vector field. This means that the magnetic field has both a magnitude (magnetic field strength) and a direction associated with every point in space. We can build a map of the behavior of the magnetic field by using magnetic field lines. For the Electric Field Measurement lab, you determined the electric field lines by finding the equipotential lines. You will determine the magnetic field today by using both a compass and a Hall probe, which is a sensor chip hooked to a computer that can measure the strength of the magnetic field at its location.

The magnetic fields that you will study today can be thought of as dipole fields. As the name suggests, a dipole consists of two types of poles. Magnetic poles are commonly given the names north and south. In fact, the magnetic field of the earth is a dipole field. To be exact, one should note that the geographic north pole of the earth is actually a magnetic south pole. Magnetic field lines always exit from north poles and enter into south poles. You have encountered another type of dipole in the Electric Field Measurement lab, which was the electric dipole. This is a positive point charge separated from a negative point charge, held apart by a fixed distance.

Magnetic fields tend to align magnetic dipoles so that the north pole of the dipole points along the magnetic field direction and the south pole points in the opposite direction of the magnetic field. This is the basic principle behind the operation of a compass. In today’s lab, you will take advantage of the fact that compasses are just magnetic dipoles aligning with whatever external field that is present, whether that is the earth’s field or another stronger magnetic field that may be present.

II. Magnetic Field Maps

Magnetic field maps consist of a series of magnetic field lines. Just as we saw for electric field lines, these lines show us both the strength and the direction of the magnetic field. In the following two exercises, you will get a sense of how the magnetic field lines behave in the vicinity of the two types of magnets. For the permanent bar

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GEOG/PHYS 182 Magnetic Field Measurement

magnet, you will sense the direction of the magnetic field using a small compass. For the Helmholtz electromagnet, you will measure the magnitude of the magnetic field using a special sensor called a Hall probe.

The Hall probe sensor measures the component of the magnetic field that points perpendicular to its plane. The positive direction for magnetic fields is shown in the Figure 1. This sensor can be used to measure magnetic field magnitudes up to 6.00 mT. The sensor is interfaced with the computer program Logger Pro to take data and plot it on several different types of graphs.

Figure 1

Exercise 1:Materials needed:1) Bar magnets2) White sheets of paper and pencil3) Compasses (careful not to reverse magnetize)

A magnetic field is a kind of aura that surrounds magnets. Although it can’t be seen directly, the overall shape can be seen by the effect it has on iron filings.

Purpose: In this activity, you will explore the patterns of magnetic fields around the bar magnets in various configurations. You will also compare the field lines produced with iron filings to those produced using a compass about a single bar magnet.

Mark the North and South magnetic poles of your magnet on the paper. Make sure you stay away from any other magnets, electrical circuits or iron materials as you do this.

WARNING: Don’t rely on the painted arrows on the pointers in the compass to tell which pole is North and which is South; they don’t all use the same convention. Make sure the pointers can rotate freely.

CASE 1: Sketch the pattern of the magnetic field using a bar magnet on a sheet of paper like this.

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GEOG/PHYS 182 Magnetic Field Measurement

A. Construct Field Line #1: Place a compass near one end of the magnet. (DO NOT touch the compass to the magnet!) Make two dots on the paper, one at the end of the compass needle next to the magnet and the second at the other end of the compass needle. Now move the compass so that the end of the needle that was next to the magnet is directly over the second dot, and make a new dot at the other end of the needle. Continue this process until the compass comes back to the magnet or leaves the edge of the paper. Draw a line through the dots and indicate with an arrowhead the direction in which the North end of the needle pointed, as shown below

B. Construct Field Line #2: Repeat the process described above, but this time, start with the compass near the magnet approximately 1 cm (1/2 inch) in from the same end of the magnet that you used above. C. Construct remaining field lines: Repeat this process until you have a picture of the magnetic field pattern all the way around the magnet. Sketch at least 6 lines, including at least 2 on each end.

Question 1 Most of your field lines come back to the bar magnet, but some of them wander off and never come back to the bar magnet. Which part of your bar magnet do the ones that wander off never to return come from? What’s going on?

CASE 2: Sketch the pattern of the magnetic field below.

A. Place two bar magnets in the configuration shown above. Be sure there is space for 3 compasses between the magnets without touching either magnet.B. Sketch the magnetic field pattern using the procedure described above.

CASE 3: Sketch the pattern of the magnetic field below.

N S

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GEOG/PHYS 182 Magnetic Field Measurement

A. Place two bar magnets in the configuration shown above. Be sure there is space for 3 compasses between the magnets without touching either magnet.B. Sketch the magnetic field pattern using the procedure described above.

Questions:1. A magnetic field is strongest where it has the most lines of force. Where is the field strongest around

a magnet?

2. Do any of the lines of force sketched in cases 1, 2, or 3 cross each other?

3. Without using a compass, sketch the pattern for the magnetic field for the following:

a.

b.

N N

N S S N

N S SS

N S

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GEOG/PHYS 182 Magnetic Field Measurement

Does this pattern show attraction or repulsion field lines? [Circle one]

c.

Does this pattern show attraction or repulsion field lines? [Circle one]

d.

4. Check your answers using a compass and sketch the pattern for the magnetic field for the following:

a.

b.

c.

N S

S N

N S S N

N S SS

N S

N

N S

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GEOG/PHYS 182 Magnetic Field Measurement

d.

5. A single bar magnet has 5 paper clips hanging off of the north pole side. What pole is induced in the bottom most side of the paper clip, north or south?

Draw a sketch and label north and south poles for the bar magnet and each of the paper clips.

Exercise 2: Measurement of the Magnetic Field Magnitude for a Helmholtz Electromagnet

N S

S N N

N

N S

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GEOG/PHYS 182 Magnetic Field Measurement

Materials needed:1) Hall probe and LabPro interface with USB cable and power cord 2) Computer with Logger Pro software3) DC power supply4) Ammeter (DMM on the 10 A range)5) Compass, Helmholtz coils, and small disk magnet6) white sheets of paper

Procedure:1) Connect the DC power supply to the Helmholtz coils. Use the DMM to function as an Ammeter on the 10 A range to read the current through the coils. Set the power supply to deliver 3.0 A of current through the coils.

2) Use the compass to construct a map of the magnetic field lines in the horizontal plane that passes through the center of both coils. You can hold the compass by hand in a horizontal plane centered in the coils. Sketch enough field lines to capture the basic trend. Figure 3 shows a few of these field lines.

Figure 3

3) Bx vs. I: Position the Hall probe sensor so that it is on the x-axis of the coils at a point midway between them, which is the origin of the x-y coordinate system shown in Figure 4. Orient the sensor so that its plane is perpendicular to the x-axis. Open the Logger Pro program. In order to have the computer plot magnetic field magnitude vs. current, you must set the program for “events with entry”. To do this, go to the EXPERIMENT menu and select Data Collection. When the New Window appears, click on the Mode and choose “events with entry”. You will then be asked to define a new column for the variable you are going to enter, which in this case is current read from the DMM.

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GEOG/PHYS 182 Magnetic Field Measurement

Figure 4For the Full Name enter Current and for the Short Name enter I. For the units enter A. Click the OK box and a blank graph with magnetic field on the vertical axis and current on the horizontal axis will appear. Set the limits of the vertical axis scale from -5 mT to +5 mT. Set the horizontal scale from 0 to 2.50 A.

When you hit COLLECT, a new window will pop up asking you whether to keep the field measurement. When your current is set where you want it, click “keep” and then enter the value of the current in the pop-up box. Start from zero current and increase it in increments of 0.25 A until you reach 2.50 A. You should now have a graph of Bx vs. I. Print this graph.

4) Bx vs. x: Go to the DATA menu and select “Delete Column”. Delete the Current column you created above. Create a new “events with entry” experiment, only now define a column for x position using units of cm. The horizontal axis scale for x should range from 0 to 25 cm.

With the magnetic sensor positioned as in the previous section, set the current to 2.50 A. This is the current that you will use for all the measurements in this section. Press the COLLECT button and enter 0 for x. Move the sensor to the x = 2 cm position without changing the orientation of the sensor and enter that value for x. Continue increasing the x position by 1 cm until you reach x = 24 cm. You will now have a graph of Bx vs x. Print this graph.

Questions:1) The electric dipole consists of a positive charge separated by a negative charge, held apart by a fixed distance, where each of the charges can be thought of as an electric monopole. The magnetic dipole consists of a north pole and a south pole, as in the bar magnet. Is it possible to find magnetic monopoles in nature? Consider what happens when you break a bar magnet into two equal pieces.

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GEOG/PHYS 182 Magnetic Field Measurement

2) Discuss other possible ways to measure the magnitude and direction of a magnetic field.

3) Compare the magnetic field of the bar magnet to the field of the Helmholtz coils. How large did you measure the region of uniform field at the center of the coils to be?

4) The magnetic field at the center of the Helmholtz coils is given by

where n is the number of turns in each coil, I is the current through the coil wires, R is the coil radius and μ0 = 4π x 10-7 Tm/A. Estimate the values of n and R from today’s lab and calculate the field at the center of the coils for a current of I = 3 A.

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