# Investigating the Magnetic Field in a Coil

How does the coil's arrangement effect the field strength?

Purpose: Investigate how the strength of the field is affected by the number of coils per unit length in a coil.

Equipment:

1. Select a slinky and stretch it between two cardboard supports. Do not over stretch the slinky!!
2. Connect a DC power supply to the ends of the slinky.
3. Insert a Multi-meter into the circuit and connect it to measure the current. Keep the current constant. Don't forget to record its value.
4. Count the number of coils between the cardboard supports and record this value.
5. Measure the distance between the supports.
6. Assemble the CBL, TI-82, and magnetic field sensor: be sure that all cables are firmly and gently in place.
7. Support the sensor and place it in the center of the slinky.
8. Use the PHYSICS program in the calculator to collect data. Use the High(mTesla) setting and collect data with choice #3; TRIGGER/Prompt
9. For each reading of magnetic field strength, vary the distance that the coil is stretched between the cardboard supports. Don't forget to record the distance for each corresponding magnetic field.

Analysis:

1. Construct a graph of Magnetic Field Strength vs Coils/Unit Length. You may download L1 using the graph link or enter the data in a spreadsheet or graph on your calculator.
2. Find the equation that describes the relationship between Magnetic Field Strength and Coils/Unit Length. Remember that y and x may not be used as variables and that units must accompany all constants. What is the meaning of the y-intercept and the slope of this graph?

Qualitatively explain why this relationship makes sense. Why should it be true that twice as many coils in a given length results in the corresponding change in magnetic field.

Extensions: A further investigation might be to see how the field strength is related to the diameter of the coil. You could use different size slinkies or springs with the same number of coils and see how the field changes with current level. Be sure to compare it to a coil with the same number of coils per unit length.

Qualitatively and Quantitatively Map the Field. Place butcher paper under the coil and use the probe to measure the field at different locations in the coil, at its ends, and in regions surrounding the coil. Also place the probe at different angles. Remember the probe must be perpendicular to the field so at the ends try rotating the probe and look for the maximum reading at a location.

Teacher Notes:

Sample data taken from a CBL, entered in Excel and graphed. Similar data was taken using a computer interface, but no advantage in using this method appeared in the data.

 Magnetic Field Length Coils/Length mTesla meters 1/m 0.024 1 40.0 0.04 0.9 44.4 0.052 0.8 50.0 0.076 0.7 57.1 0.085 0.6 66.7 0.111 0.5 80.0 0.156 0.4 100.0 0.225 0.3 133.3 0.322 0.2 200.0

Written by Christine Deyo, July 1997