Mapping the Magnetic Field

Safety and Equipment No special safety precautions are necessary for this lab. Paper and pen/pencil Computer with PASCO 850 Universal Interface and PASCO Capstone PASCO 2-Axis Magnetic Field Sensor Two Banana-to-Alligator Wires (for Signal Generator) Solenoid Coil Set of small compasses Horseshoe magnet, bar magnet

Note: This lab should be written up with the “Full Report” format. See the Lab Syllabus area of Blackboard for a description of the format.

IntroductionThe gravitational field or electric field of a point mass or charge is radial, meaning it points outward or inward. The magnetic field of a magnet consists of complete loops that surround and go through the magnet. Magnetic fields always form looped patterns. Each loop goes through the object causing the magnetic field. Any point on the object where the field emerges (points outward) is called a “North” pole, while a spot where it points toward the object is a “South” pole.

A compass needle is a magnet that is free to rotate. It tends to rotate so that its north pole points in the same direction as an external magnetic field. We will use compasses to find the direction of the magnetic field in various situations.

The strength of a magnetic field decreases with the distance from the magnet. The strength of the magnetic field could vary inversely as the square of distance, as with the strength of a gravitational field or an electrical field. However, it is not always the case and the strength of the magnetic field could vary in a different way relative to distance.

We expect that the magnetic field inside a solenoid coil will be found by the equation:B=μ0∋¿ lwhere μ0=4 π ×10−7 T ⋅m/ A is a universal constant, N is the number of loops of wire, and ℓ is the

length of the coil. Outside the solenoid, the field should be weaker than this.

Objective:Determine the direction and the magnitude of the magnetic field around two permanent magnets and a solenoid.

Exercise #1: Permanent “Horseshoe” magnet.1. Place a “horseshoe” permanent magnet flat in the middle of a blank sheet of paper.2. Use a pencil to trace the shape of the magnet on the paper.

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3. Place small compasses evenly around the magnet in such way that that the arrows form one continuous line. See Figure 1.

4. Trace out the magnetic field line formed by the compasses. To do this, remove the compasses one by

one, while drawing the exact direction of the arrow on the paper.5. Repeat 3−4 for at least four different lines starting at different point of the magnet. See Figure 16. Determine and label the poles of the magnet on each sketch. (Note: Sometimes the compasses get

“reversed”. Use an agreement among several compasses to determine the direction of a magnetic field line.)

7. Take a picture of the final drawing or scan it for the report.8. Stand the magnet vertically on end on another blank sheet of paper and repeat steps 2–7.

Exercise #2: Permanent “Bar” magnet.1. Repeat Exercise #1 (steps 2–7) for the permanent “bar” magnet laid flat on a blank sheet of paper. (You

don’t have to stand the bar magnet on its end.)2. Take a picture of the final drawing or scan it for the report.

Exercise #3: Solenoid1. Place the solenoid on a blank sheet of white paper and mark the ends and the sides of the solenoid. Use

two wires to connect a solenoid to the PASCO 850 Universal Interface Output 1.2. Use the “Magnetic Field.cap” file or open PASCO Capstone and set up the Signal Generator for DC

Voltage on Output 1. Set the DC Voltage to 10.0 V with a 0.55 A current limit.3. Turn the Signal Generator on. 4. Repeat Exercise #1 (steps 2–7) for the solenoid. (You don’t have to stand the solenoid on its end.)5. Investigate how the orientation of the compasses’ arrows changes if the current through the solenoid is

reversed. State your findings.

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Figure 1. Horseshoe magnet with compasses measuring the magnetic field direction.

Exercise #4: Strength of the magnetic field.

1. Connect the PASPort 2-Axis Magnetic Field Sensor into PASPort 1 on the 850 Universal Interface.2. Use the “Magnetic Field.cap” PASCO Capstone file to load the settings and displays appropriate for the

magnetic field measurement.3. Turn on the Signal Generator, it should be set for 10 V DC. (The actual voltage may be lower because

of the current limiter.)4. Press Record so that the Capstone displays update in realtime.5. Make note of how much current flows through the coil.6. Measure the length of the coil (blue double-arrow in the figure).7. Visually estimate the number of loops of wire in the coil. 8. Measure the maximum magnetic field of the coil.

Hold the Magnetic Field Sensor far away from any source of magnetic fields and zero the sensor by pushing the TARE button on the sensor box.

Insert the sensor rod into the center of the coil (see Figure 2). Move the sensor around inside the coil to see if the position of the sensor changes the reading.

9. Move the sensor out 1 cm from where the previous measurement was. Record the magnetic field.10. Repeat Step 9 until the field gets to zero.11. Graph your measurements of B vs. x (the distance from the initial point).12. Measure the maximum magnetic field for the horseshoe magnet, the bar magnet, and the solenoid coil.

Make note on the drawings of where these measurements were found.13. Using the maximum magnetic field of the coil, the measured current, calculate the number of loops of

wire in the coil.

Conclusions: Compare the shapes of the magnetic fields of the horseshoe magnet, bar magnet, and solenoid coil.

Which permanent magnet does the solenoid most resemble? Compare your calculation of N to the estimate you made in Step 6. Compare the maximum magnetic field strengths of the horseshoe magnet, bar magnet, and solenoid coil.

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Figure 2.

Evaluate and state whether the goal of the experiment was accomplished.

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