AP Physics Lab – Magnetic Field of a Solenoid

Purpose

The goal of this lab exercise is to “discover” the properties of the magnetic field of a solenoid. You will determine the direction and shape of the magnetic field lines. And you will investigate the effect of several variables on the magnetic field strength.

Procedure

The basic setup consists of a steel “slinky” connected to a DC power supply and a magnetic field sensor connected to a lab interface and monitored with Logger Pro software running on a laptop. Complete all connections before turning anything on.

The magnetic field sensor should be switched to the Low amplification setting. The current through the solenoid is adjusted and monitored by the power supply. Do not exceed 3 amperes. It is good practice to turn the power supply all the way down whenever you make changes to the setup. Note: at all times the slinky must be stretched enough so that the coils of the slinky do not touch one another – this would reduce the resistance, lead to high currents, and prevent the current from moving in the helical fashion that is a defining characteristic of a solenoid. (The wire in a more practical solenoid would have insulation and the coils could be very close together and even touch.) The effective length of the solenoid is the distance between the electrical connections where the current enters and leaves.

Part A – Mapping the Field

Stretch the slinky to convenient amount and establish a current of 2.00 A through its entire length. Use a magnetic compass to probe the resulting field. Test areas around the outside and along the inside of the solenoid. You may attach the compass to the end of a meter stick in order to test the inside areas of the coil. Try reversing the direction of the current. Sketch the field with the correct orientation to the current.

Use the magnetic field sensor to measure the strength of the magnetic field at various points inside the solenoid. Note: you must zero the sensor prior to measurements to get a correct reading. To get a proper reading the sensor must be rotated so that the white circle on it points in the same direction as the field (put another way, rotate the sensor so that the magnetic flux through the white circle is maximized). Record the values at various positions in your sketch of the field. Also determine the length and number of turns and record these values.

Part B – Magnetic Field Strength vs. Current

Keep the same “geometry” used in Part A. Use the equipment to measure the field strength at the center of the solenoid. Adjust the current and use the computer to produce a graph of magnetic field strength vs. current. Obtain an appropriate regression equation. Sketch the resulting graph and record the equation on your data sheet.

Part C – Magnetic Field Strength vs. Number of Turns

Without changing the effective length or the current, adjust the number of turns and observe the change in the magnetic field strength measured at the midpoint. Note: in order to change the number of turns but retain the same length you must change the amount of stretch and the points of connection. Careful! Always reduce the voltage to zero whenever you change the connections. By decreasing the number of turns you also decrease the resistance which could lead to a current overload – you will need to adjust the power supply accordingly to get the desired current.

Part D – Magnetic Field Strength vs. Length

Without changing the number of turns or the current, adjust the length and observe the change in the magnetic field strength measured at the midpoint. Note: in order to make this happen simply leave the connection points unchanged and then change the amount that the slinky is stretched so that the two connection points are separated by a different distance. Remember the effective length of the solenoid is the distance between the connection points.

Questions

1. What type of relation exists between magnetic field strength and current? Support your answer by referring to the results.

2. What type of relation exists between magnetic field strength and number of turns? Support your answer by referring to the results.

3. What type of relation exists between magnetic field strength and length? Support your answer by referring to the results.

4. Based on your results and observations what would be an appropriate single equation for determining the magnetic field inside a solenoid. Your equation should give B as a function of μ₀, I, N, and L (the permeability constant, current, number of turns, and length). Hint: use unit analysis and the types of relations that you discovered.

5. Use your equation to calculate the fields measured in parts A, C, and D and calculate the percent difference in the measured values.

6. Use the slope from the graph in part B to determine the value of μ₀ and determine the percent error.

Data/Observations:

Part A – Mapping the Field

Length = # of Turns =

Part B – Magnetic Field Strength vs. Current

Regression Equation:

Part C – Magnetic Field Strength vs. Number of Turns

Current = 2.00 A Length = 0.800 m	Number of Turns	Magnetic Field Strength (mT)
	200
	150
	100

Part D – Magnetic Field Strength vs. Length

Current = 2.00 A # of Turns = 100	Length (m)	Magnetic Field Strength (mT)
	0.800
	0.600
	0.400