Materials Included In Kit

Additional Materials Required

Safety Precautions

The materials in this lab are considered nonhazardous. Use care when handling the strong magnets. The magnets can quickly snap together, resulting in pinched fingers or cracked magnets. Remind students to wash their hands thoroughly with soap and water before leaving the laboratory.

Disposal

The materials should be saved and stored for future use.

Lab Hints

• Enough materials are provided in this kit for 16 students working in pairs or for eight groups of students. All materials are reusable. The laboratory experiment can reasonably be completed in one 50-minute class period.
• Students should not measure the separation distance for Total Mass forces greater than 250 g (2.5 N). Once the magnets are very close together, the force becomes too strong and the separation distance varies by too small a value to accurately measure the separation distance with an ordinary metric ruler.
• The mass of the large container and magnet are also incorporated into the Total Mass registered on the spring scale (typically around 25 g). When using a 500 g/5N spring scale, this small mass is barely noticeable. However, for more accurate Total Mass (force) measurements, the mass of the large container and magnet should be measured. This value should then be subtracted from the value registered on the spring scale to determine the “true” Total Mass.
• If manufactured 100-g and 200-g hooked weights that will fit inside the small container are available, these may be used instead of the support stand and spring scale setup. The weights may be stacked on top of the small container so long as they remain balanced. Nonferrous (nonmagnetic) weight sets are ideal. Students can measure the separation distance between the magnets by holding the apparatus in their hands at eye level. The apparatus must be held upright and the floating chamber must remain balanced inside the container when the students take the distance measurements.
• Students should read the Background and Procedure before starting the experiment.
• The constant of proportionality (A), which represents the magnetic moment between the two dipole magnets, can also be calculated from the log–log graph. Students can extrapolate to determine the y-intercept (b) on the log–log graph. Students can calculate the value of A using the following expression: b = [log(A)]/n.

Teacher Tips

• Some students may not be familiar with logarithms, or logarithm graph paper. Students may either calculate the logarithm (log) using their calculators and plot these calculations on normal graph paper, or they may plot the data points directly onto log-log graph paper. A log-log plot will make any exponential function linear.
• Free online graph paper can be designed at the following website: www.incompetech.com/beta/plaingraphpaper/ (accessed July 2018).
• Thorough explanations of magnets and magnetic fields can be found in any physics or physical science textbook. The Background information provided is only a brief description.

Sample Data

Mass of small container and magnet: ___10 g___
Mass of PVC tube: ___30 g___

Answers to Questions

1. Graph the Separation Distance versus Total Mass on normal graph paper. Draw a best-fit straight or curved line through the data points. Describe the shape of the best-fit line.
   {12551_Answers_Figure_1}

   This graph shows an inverse exponential-type relationship between the separation distance and the Total Mass (force) between the magnets.

2. Calculate and graph the log of the Separation Distance versus the log of the Total Mass on graph paper. Record the calculations in the data table. Draw a best-fit line through the data points.
   {12551_Answers_Figure_2}
3. Calculate the slope of the best-fit line on the log–log graph plot.

   The log–log graph shows a straight line relationship. The slope is calculated by dividing the “rise by the run” of the best-fit line. For this data, the slope is –0.38. (This is close to the expected value of –0.33.)

4. What does the slope of the line indicate?

   The slope of the line shows the inverse exponential value for the separation distance, as described in Equation 2.

5. Calculate the value of n by taking the inverse of the magnitude of the slope determined in Question 3. Compare the relationship between the force due to a magnet and the separation distance, and the relationship between force due to gravity and the separation distance. Does this result make sense based on your experiences with magnets and gravitational force? Explain.

   The value of n is equal to 1/0.38 which equals 2.6. This value is close to the predicted value of 3 for dipole magnets. The value of n for gravitational and electrostatic forces is equal to 2. The force due to a magnet decreases faster with distance compared to the force due to gravity. This makes sense because the force from a magnet is very strong when the magnets are close to each other. The force is much stronger than the force due to gravity between the two objects. When the magnets are moved even 10 cm away, the force due to magnetism is almost nonexistent between the two magnets.

Introduction

The force due to gravity between two massive objects and the force due to electrostatic charge between two electrical charges behave similarly. In both cases, when the distance between the two objects changes, the change in magnitude of the force is inversely proportional to the distance between them (F ∝ 1/d²). Discover the relationship between the force due to magnetism exerted by two repelling magnets and their separation distance.

Concepts

• Magnetic force
• Logarithm
• Magnetic properties
• Graphing

Background

Forces hold the universe together. Everything from huge galaxies to tiny atoms are held together by the one or more of the four “fundamental” forces—strong and weak nuclear forces, gravitational force, and electromagnetic force. While it is not possible to “see” a force, the effect that forces have on objects can be observed and studied. In this experiment, the effect of the magnetic force will be apparent as one container “floats” inside another container in seeming defiance of the force due to gravity. The force due to gravity and the force between two magnets each depend on two properties—an intrinsic property of the material (i.e., an object’s mass for gravitational force and the magnetic moment of a magnet), and the distance between the objects.

The force due to gravity is always attractive. Any two objects will be pulled toward each other due to their gravitational attraction. For objects that have a small mass, the force due to gravity is practically unnoticeable and requires special equipment to measure. In order to produce noticeable gravitational forces, massive objects the size of moons and planets are required.

Electric charges can be either positive or negative and can exist independently of one another. In contrast to gravity, the electrostatic force can be either repulsive or attractive, depending on the charge polarity on the respective objects. Two “like charge” objects will repel each other, whereas unlike charges will attract each other. Regardless of whether the force is attractive or repulsive, the electrostatic force depends on the magnitude of charge on the objects, and the inverse square of the separation distance (1/d²).

Similar to electric charges, magnets also have two different “signs,” or polarities which are referred to as the north pole and the south pole. However, these magnetic “charges” do not exist independent of one another. No matter how small a magnet is, it will always have a north pole and a south pole. There has not been any conclusive evidence of a single-poled magnet, or monopole. Just like electric charges, two similar magnetic poles repel each other (i.e., a north pole will repel a north pole). Two opposite polarities will attract each other.

For both the gravitational and electrostatic force, the mathematical relationship between the magnitude of the force and separation distance can be written in the form:

F = force
A = constant of proportionality
d = separation distance

For example, if the force due to gravity between two objects separated by 1 cm is equal to 10 Newtons, then the force due to gravity when the objects are separated by 2 cm will decrease by a factor of 4, and will be equal to 2.5 Newtons.

In this experiment, the mathematical relationship between the magnitude of the magnetic force and the separation distance between two magnets will be determined using dipole magnets. The general expression can be written:

F = force
A = constant of proportionality
d = separation distance
n = exponential factor

This expression can also be written in logarithm form by taking the log of both sides: In logarithm form, an exponential equation (Equation 2) becomes a linear equation (y = mx + b). In the linear equation, log (d) represents “y,” log (F) represents “x,” –1/n represents “m,” and [log (A)]/n is a constant and represents “b.”

Experiment Overview

Measure the separation distance between two dipole magnets subjected to a compressing force (mass). By plotting the log of the separation distance versus the log of the force (mass), the slope of the line can be calculated. Take the inverse of the magnitude of the slope to determine the exponent (n) to see the relationship between force and distance between two dipole magnets.

Materials

Safety Precautions

The materials in this lab are considered nonhazardous. Use care when handling the strong magnets. The magnets can quickly snap together, resulting in pinched fingers or cracked magnets. Wash hands thoroughly with soap and water before leaving the laboratory.

Procedure

1. Obtain two neodymium magnets, the small and large plastic containers, and transparent tape.
2. Securely tape one of the magnets to the bottom of the large container on the outside. Make sure the magnet is in the center of the bottom of the cup. Use 2–3 pieces of tape to secure the magnet.
3. Repeat step 2 using the second magnet and the smaller container. Initially, use only one piece of tape.
4. Test the orientation of the magnets. Place the small container inside the large container. The two magnets should repel each other and the small container should “float” inside the large container. Note: If the two magnets attract each other, remove the tape from the small container and flip the magnet over.
5. Once the magnets are in the proper orientation (they repel each other), use 2–3 pieces of tape to secure the magnet to the bottom of the small container.
6. Place the small container with the secured magnet on a balance and record the mass to the nearest gram in the data table on the Measuring Magnetic Force Worksheet.
7. Place the PVC tube on the balance and record the mass to the nearest gram in the data table.
8. Use scissors to cut approximately 30 cm of string.
9. With transparent tape, secure one end of the string to the side of the large container near the top (see Figure 1). Use 2–3 pieces of tape to prevent the string from slipping.
   {12551_Procedure_Figure_1}
10. Secure the other end of the string to the opposite side of the large container so that the string is parallel, and the container will remain level and balanced when held by the string. (The string will act like a handle to the plastic “bucket.” The “bucket” cannot be tilted.) Once the string is properly aligned, use 2–3 pieces of tape to secure it completely.
11. Obtain a small paper clip and bend the paper clip as shown in Figure 2.
    {12551_Procedure_Figure_2}
12. Using a support stand and clamp, set up the apparatus as shown in Figure 1. Hang the large container at least 10 cm above the metal base of the support stand.
13. Place the small container inside the large container (it should “float”). Do not place the PVC tube inside the small container until step 15.
14. Use a metric ruler to measure the separation distance between the magnets. Make sure the small container is level, the magnets are parallel to the tabletop, and the small container “floats” in the center of the large container. Measure from the bottom of the top magnet to the top of the bottom magnet. Measure to the nearest 0.1 cm and record the value in the data table. The Total Mass will be equal to the mass of the small container and magnet.
15. Place the PVC tube into the small container.
16. Measure the separation distance between the magnets. Make sure the small container is level, the magnets are parallel to the tabletop, and the small container “floats” in the center of the large container. Measure from the bottom of the top magnet to the top of the bottom magnet. Measure to the nearest 0.1 cm and record the value in the data table. The Total Mass will be equal to the mass of the PVC tube plus the mass of the small container and magnet.
17. Push down on the PVC tube until the spring scale registers 100 g (1 N).
18. Measure the separation distance between the magnets. Make sure the small container is level, the magnets are parallel to the tabletop, and the small container “floats” in the center of the large container. Measure from the bottom of the top magnet to the top of the bottom magnet. Measure to the nearest 0.1 cm and record the value in the data table. The Total Mass is equal to the value registered on the spring scale.
19. Repeat steps 18 and 19 for the 150-g, 200-g, and 250-g Total Mass forces as shown in the data table. Record all the appropriate values.
20. Consult your instructor for appropriate storage procedures.

Student Worksheet PDF

12551_Student1.pdf