Biot Savart s law
1 Objective The objective of this experiment is to verify Biot-Savart s law for certain geometries. Over the course of the preparation, the actual experiment and the writing of the report you will gain basic knowledge on how to conduct experimental measurements. These include, how to determine error sources and how to take them into account in your measurement. You will also learn how to set up an experiment in order to verify a given assumption. 2 Experimental Equipment You will design an experiment allowing you to test Biot-Savart s law. The necessary equipment is provided, but you must figure out how to assemble it yourselves. Never switch on the equipment without the assistants explicit authorization! The available equipment and description of the basic functions is listed below (in random order): 2 meter 15-pole extension cord depicted in figure 1. Figure 1: 2 meter 15-pole extention cord. 1
Power supply with continuously adjustable output between 0V and 24V or 0A and 20A (see figure 2). You can adjust either set voltage or current. The applied voltage and current are displayed on the device. Figure 2: Power supply. Holder for plug-in elements shown in figure 3. Includes a support rod allowing it to be attached with another element. Figure 3: Holder for plug-in elements 2
Optical bench (see figure 4). It is 75 cm long and has a scale on it. Figure 4: Optical bench 2 clamping arms depicted in figure 5. They allow to connect rods or bars at 90 angle. Figure 5: Clamping arm. One red and one blue cable (1m) for electrical connections (an example of a red cable is shown in figure 6). Figure 6: Red cable. 3
One straight and three loop conductors (see figure 7). The straight conductor is 40cm long. The circular conductors have radii of 2, 4 and 6 cm. Figure 7: Different conductors. Universal measuring instrument (figure 8). In combination with the correct sensor, many different physical quantities, such as force, acceleration, magnetic flux density, pressure or temperature can be measured. The sensors are automatically detected. Figure 8: Universal measuring instrument. 4
A Hall effect probe depicted in figure 9. This device includes two hall sensors allowing measurements along the axis of the probe and along a single axis perpendicular to it (radial direction). Measurement error: ±2% plus 0.5% of the range limit value. Figure 9: Hall sensor. 3 Before the experiment You will build the experimental setup yourself using the equipment described in the previous section. Before the experiment, you must consider how to design the experimental apparatus and what quantities you will measure. Use Biot-Savart s law to derive an mathematical expression for the geometries in your setup. What variables does your measured quantity depend on? What dependencies can you verify? Think about possible error sources and perform the error analysis that will show you how these errors will influence your measurement. How sensitive the errors are with respect to the variable? When you re preparing the measurement, think and if needed write down, the following:: The derivation of the expressions you will verify, starting from Biot-Savart s law. Refer to the course book, i.e. what is the equation you start with and where can it be found? The experimental setup. How do you assemble the parts? How does it work? You can make sketch of your setup. What quantity will you measure, and as a function of what? What will you plot? Are there any natural constants you can determine? An error calculation, resulting in a formula for the error of the measured quantity as a function of the measurement variables errors. What are possible error sources? This measurement plan needs to be completed before the experiment and will be checked by the assistant before you can start. It is also advisable to prepare excel tables to write down your results. 5
4 During the experiment When you arrive to the session, present your experimental setup to the assistant and hand in your measurement plan. The assistant will check your planned setup and you will be given time to build it yourselves. Once you are done, have the assistant check your setup. Never switch on the equipment without the assistants explicit authorization! Once the assistant has checked the setup, you can start measuring. Write detailed notes of the values you measure, especially the values of the quantities you set or measure. After you have completed the experiment, ask the assistant to check that you have performed the necessary experiments. This is a good time to ask questions. 5 After the experiment After the experiment you should write a report of maximum of 7 pages (excluding title page and references) where you describe the experiment and present your results. Introduce the theoretical background, and show the derivation of the expressions you obtained from Biot-Savart s law and the corresponding error calculations briefly. Pay attention to the graphical representations. Try to present your findings in one or two well designed graphs. The report should include, preferably in this order: The derivation of the expressions you have verified, starting from Biot-Savart s law. Refer to the course book, i.e. what is the equation you start with and where can it be found? If applicable, the derivation of the expression giving you a universal constant. An error calculation, resulting in a formula for the error of the measured quantity as a function of the measurement variables errors. The experimental setup. Explain the setup and your experimental procedure. What are possible error sources? Estimate how big they are. Compare the influence of different error sources. How could you improve the accuracy? Present your results in graphical format. Remember to describe your results. Just showing the data is not enough. If applicable, what is the value of the universal constant you derived? How do your results compare to literature values? During the experiment, you explore the field created by a conductor when a current is passed through it. This method is used for example in magnetic data storage. Write a small essay (about 1 page) on magnetic data storage technology considering the writing and reading procedures and its relation to the Biot-Savart law. 6