Magnetic Fields: Solenoids & Helmholtz Coils

Lab #22 Prof. Susanne M. Lee Magnetic Fields – Solenoids & Helmholtz Coils page 1 University at Albany, SUNY Magnetic Fields: Solenoids & Helmholtz...
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Lab #22 Prof. Susanne M. Lee

Magnetic Fields – Solenoids & Helmholtz Coils

page 1 University at Albany, SUNY

Magnetic Fields: Solenoids & Helmholtz Coils Reading: Giambatista, Richardson, and Richardson – Chapter 1 (1.4, 1.6-1.9), Chapter 19. Summary: In the previous lab, a Helmholtz Coil was used to generate the magnetic field, which depended quite strongly on position. There are times when a very uniform magnetic field, independent of position, is desired. For example in Nuclear Magnetic Resonance (NMR) or Magnetic Resonance Imaging (MRI), the primary, strong, magnetic field must be uniform over the whole sample – or patient in MRI. Creating such a uniform field is analogous to creating a uniform electric field using capacitor plates (see Lab 10). However for magnetic fields, two parallel plates will not produce a uniform magnetic field; a long solenoid is needed. In applications such as MRI, it has been determined through experimentation the needed magnetic field strength to produce the proton spin flipping necessary for clear imaging. So how many coils of wire are needed to produce a specific strength magnetic field? In this lab, you will experimentally measure the magnetic field strength of a solenoid and pair of Helmholtz coils. From their response to different applied currents, you will determine the number of turns in the solenoid and Helmholtz coils (from Lab 15) – you will not count the turns – needed to produce the measured magnetic field strengths. Note: Answers to all questions are to be given in full sentences, such that by looking at the answer, the reader knows what question is being answered without having to read the question. Any answers not written this way, even if they are correct, will receive 0 credit. Pre-Lab Analysis 1.) Read Chapter 1 and do problems #7, 9, 35, 52, and 55. I recommend you read the whole chapter, but you are responsible for only the sections listed above. [25!pts]1 In this week’s lab, you will begin by measuring the field generated by a solenoid. The field strength in a solenoid is governed by the amount of current going through each turn of the solenoid. 2.) Look up in your textbook the equation that relates the magnetic field (B) produced by a solenoid to the current I in each turn (or loop) of the I!(A) B!(mT) solenoid. 1.75 4.617 1.50 3.863 A. Record this equation in your notebook, making sure to 1.25 3.085 define every term in the equation. [7!pts]2 1.00 2.476 B. If you plotted B on the y-axis and I on the x-axis, what 0.90 2.259 would your graph look like? What would be the slope 0.80 2.033 of this graph in terms of µ0 and n? [6!pts]3 0.70 1.779 0.60 1.545 3.) Table 1 contains current and magnetic field data taken with 0.50 1.380 a solenoid. 0.40 1.086 0.30 0.779 A. Which values in the table have the least number of 0.20 0.545 significant digits (see Pre-lab Question 1)? How many 0.10 0.308 significant digits do these values have? Explain how you arrived at your answer. [9!pts]4

Table 1: Solenoid data.

Lab #22 Prof. Susanne M. Lee

Magnetic Fields – Solenoids & Helmholtz Coils

page 2 University at Albany, SUNY

B. Graph the data in Table 1 and fit a line to it. Print your results. [4!pts]5 C. From your fit, calculate the number of turns per cm (n) and from that number find the total number of turns (N) in the solenoid, if the total solenoid length is 1.4!m. Show all your work; don’t forget units and significant digits in your answers. [13!pts]6 In the second part of this lab, you will measure the magnetic field generated by a set of Helmholtz coils (the same ones you used in Lab 4). 4.) Write the equation that relates the magnetic field (B) produced by a set of Helmholtz coils to the current I in each turn (or loop) of the coils (see Lab 4). Suppose the average radius of the coils is R and there are N total turns in the coils. (4 pts)7 5.) Table 2 contains current and magnetic field data taken with a set of Helmholtz coils. A. Which values in the table have the least number of significant digits? How many significant digits do these values have? Explain how you arrived at your answer. [14!pts]8 B. Graph the data in Table 2 and fit a line to it. Print your results. [4!pts]9 C. From your fit, calculate the total number of turns in the Helmholtz coils. The radii of the coils are 10 cm. Show all your work; don’t forget units and significant digits in your answers. [10!pts]10

I!(A) 2.51 2.25 2.01 1.75 1.50 1.25 1.00 0.75 0.50 0.40 0.30 0.20 0.10

B!(mT) 2.717 2.384 2.076 1.960 1.546 1.339 1.057 0.808 0.536 0.411 0.316 0.203 0.096

6.) Outline the lab following the format of “Outline Format” Table 2: Helmholtz!Coil data. posted on the Electronic Reserves web page. [20 pts]11 Equipment to be used in this lab: ¶ 2 digital multimeters ¶ 1 power supply ¶ 1 solenoid ¶ 1 pair of Helmholtz coils ¶ 1 magnetic sensor wand 1.) Equipment Set-up q The circuit will be partially pre-wired for you. q Cautions: • Under no circumstances should you make connections with the power supply on. These voltages can be dangerous. • A multimeter will already be wired in series with the current source. • Never exceed the listed voltages, to ensure solenoid and coil life.

Lab #22 Prof. Susanne M. Lee

Magnetic Fields – Solenoids & Helmholtz Coils

page 3 University at Albany, SUNY

• Turn off the power immediately, when not actually needed for the measurement. q Make sure the magnetic sensor is plugged into Din1. The switch on the back of the box should be set on the Low (x10) setting. q Click on the “Magnetic Field” icon to start LoggerPro. q Zero the magnetic sensor by holding the sensor wand over your head and clicking on the “Zero” button in the program. Do this before starting each set of measurements in the lab. You should make a note in your notebook every time you zero the sensor. [26 pts]12 2.) The Solenoid A. Current vs Magnetic Field Data q Record the green number marked on the base of your solenoid. [2 pts]13 q Record the length and mean radius of the solenoid. [6 pts]14 q Connect the red and black wires to their respective color connections on the solenoid. q Turn the voltage knob on the power supply all the way up (clockwise), and the current knob all the way down (counter-clockwise). Turn on the power supply. • If you hear a clicking noise from the current source, the power supply has reached it’s maximum current. Turn the current down until the clicking stops. q Increase the current (should be at 0A when you start) to 0.10A. q Measure the magnetic field by placing the sensor just inside the mouth of the solenoid. See the Appendix at the end of the lab for important instructions on how to orient the magnetic sensor during your measurements. q Move the sensor around while recording the strength of the magnetic field as a function of time. q After the data is taken, press the “Stat” button and in your notebook record the maximum magnetic field. q Repeat these measurements for 12 more currents ranging from 0.20 A to 1.30A in increments of 0.10 A. Record the corresponding magnetic fields in your notebook. (You should have a total of 13 rows in your table.) [28 pts]15 B. Determining the number of turns/cm & the total number of turns q In Excel plot all your solenoid data and fit a line to it. Print your results. [10!pts]16 q From your fit, calculate the number of turns per cm (n) and from that number find the total number of turns (N) in the solenoid. Show all your work; don’t forget units and significant digits in your answers. [15!pts]17 3.) The Helmholtz Coils A. Current vs Magnetic Field Data q Record the purple number marked on the base of the Helmholtz coils. [2 pts]18 q Record the mean radius of the Helmholtz coils. [6 pts]19 q Make sure the power supply is off. Disconnect the power supply leads to the solenoid and attach the red and black wires to their respective red and black connections on the Helmholtz coil base. The red positive connection will be

Lab #22 Prof. Susanne M. Lee

q

q q q

Magnetic Fields – Solenoids & Helmholtz Coils

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marked with a red plus sign and the black negative connection will be marked by a black minus sign. Turn the voltage knob on the power supply all the way up (clockwise), and the current knob all the way down (counter-clockwise). Turn on the power supply. • If you hear a clicking noise from the current source, the power supply has reached it’s maximum current. Turn the current down until the clicking stops. Increase the current (should be at 0A when you start) to 0.10A. Measure the magnetic field by placing the sensor in between the coils and click “Collect”. After the data is taken, press the “Stat” button and in your notebook record the mean magnetic field. Repeat these measurements for 12 more currents ranging from 0.20 A to 2.60A in increments of 0.20 A. Record the corresponding magnetic fields in your notebook. (You should have a total of 13 rows in your table.) [28 pts]20

B. Determining the total number of turns q In Excel plot all your Helmholtz coil data and fit a line to it. Print your results. [10!pts]21 q From your fit, calculate the total number of turns (N) in the coils. Show all your work; don’t forget units and significant digits in your answers. [11!pts]22 4.) Cleaning Up q When you are finished with your experiments and calculations, reconnect the solenoid as in the first part of the lab. All other components and equipment you used in this lab should be neatly arranged on your lab bench. q Call your TA over to check that the solenoid is correctly wired. q Once your TA has checked everything, you may leave. [5!pts]23

Lab #22 Prof. Susanne M. Lee

Magnetic Fields – Solenoids & Helmholtz Coils

page 5 University at Albany, SUNY

Appendix: Instructions for Orienting the Magnetic Sensor during Measurements q The sensor (see Figure 1) is sensitive to how white dot plastic case it is oriented with respect to the magnetic field being measured with the sensor. When the sensor is in the position shown in Figure 2, it should read zero and in the field direction position shown in Figure 3 it should read a maximum. q Check that this is so before beginning the Figure 1: Magnetic field sensor is only solenoid measurements. sensitive to fields perpendicular to the q Because of this position sensitivity, it will white dot in the rectangular sensor be difficult to position the sensor inside the embedded in the cylindrical plastic case. solenoid for a maximum reading – thus the reason for measuring the B-field close to the end of the solenoid. This is also the reason for moving the sensor around a little inside the solenoid while taking magnetic field measurements.

Figure 2: Field sensor inserted parallel to solenoid axis. Sensitive direction is perpendicular to the solenoid axis. Reading should be zero.

Figure 3: Field sensor inserted perpendicular to solenoid axis. Sensitive part of sensor (white plastic rectangle) is parallel to solenoid axis. Reading should be a maximum.