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The purpose of this experiment is to study magnetic field as a function of distance along the axis of a finite solenoid and a coil; and, to generate a voltage in a coil of wire to measure a time- varying magnetic field by using the phenomenon of Faraday induction. Magnetic field is a field of force produced by electric currents, which can be either macroscopic or microscopic. This phenomenon is the explanation as to how modern electric generators produce electricity.
Two different approaches can be used to calculate magnetic fields. The more general method is the Biot- Savart law, which states:
B= (Uo*I*dl*sin(θ))/(4π(*r)^2 ) .
According to this equation, a coil of wire that is carrying a current, I, and is smaller than the radius of the coil, R, produces a magnetic field on the axis of the coil. If the coil is rotating, a more complex form of the Biot- Savart law should be used such as:
B= (NUo I R^2)/(2(R^2+x^2 )^(3/2) ) .
In this case, x is the distance along the coil axis from the center of the coil, N is the number of turns of the wire and uo is the permeability of free space, which is equal to
1.256 x 10-6 H/m.
The other method for finding a magnetic field is by using Ampere’s Law.
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Ampere’s Law is usually used to calculate current, but if its rewritten, it can be used to calculate the magnetic field. For example,
B= μo nl
where n is the number of turns per unit length of the solenoid, and B=0 outside the solenoid.
However this equation only holds true when an infinite solenoid is being used. For a finite solenoid, which is what was used for this experiment, a different equation must be used. For example,
ε= -d/dt ∫B*dA.
The induced voltage is then observed on the oscilloscope. The amplitude of the voltage is proportional to the strength of the magnetic field.
Applications of magnetic field can be seen in everyday life even if we don’t realize it. For example, the magnets that are used on the refrigerator to hold papers, train tracks, roller coasters, and even a compass are all examples where the concepts of magnetic field can be applied.
To conduct the first part of the experiment, the oscilloscope was first properly set up and, the meter stick was inserted into the white tube. The solenoid was then connected to the function generator, which was already set up with the proper settings but, was still double checked to make sure all the settings were set right. When it was set up properly, a sine wave appeared on the oscilloscope when it was turned on. This represented the voltage induced in the search coil which was proportional to the magnetic field in the solenoid. The magnitude of the sine wave voltage that was seen on the oscilloscope was then recorded. Now, the meter stick was pushed by 5 cm increments out of the white tube to record its voltage. This was done until the field was too weak for a good signal to appear on the oscilloscope. The data was then graphed, labeling the log of the magnetic field on the y – axis and the log of distance on the x-axis. The slope was measured and compared to the theoretical slope.
For the second part of the experiment, the large coil was connected to the oscillator, and the meter stick was inserted into the other end of the tube. The magnetic field produced was measured on the axis of the large coil, and the voltage was measured as a function of the distance x from the midpoint of this coil. The diameter of the large coil was also measured. When all of the data was recorded, it was then graphed, and the slope was compared to the predicted slope from the second equation. Finally, voltage v. R2 + x2 was also graphed, taking note of the slope as well.
Measurements revealed distinct behaviors of magnetic fields along the solenoid's axis and around the coil. The solenoid demonstrated a predictable decrease in magnetic field strength with distance, aligning with theoretical expectations. In contrast, the coil's field exhibited a more complex pattern, requiring further analysis to interpret correctly.
Graphical representations of voltage versus distance for both setups illustrated the magnetic field's attenuation over distance, with slopes of plotted graphs offering a quantitative measure of this relationship.
The experimental slopes, derived from log-log plots of voltage against distance, were compared to theoretical predictions. The solenoid's data aligned closely with Ampère's Law's implications, while the coil's results necessitated a more nuanced interpretation, considering the complex interplay of coil dimensions and magnetic field geometry.
This comprehensive exploration of magnetic fields through the lens of a solenoid and a coil underscores the foundational principles governing electromagnetic phenomena. The experiment not only reinforces theoretical models but also highlights the intricate relationship between electric currents and magnetic fields. The findings affirm the principles postulated by Faraday and Oersted, illustrating the magnetic field's generation by electric currents and its spatial dependence.
The experiment's success in bridging theoretical predictions with empirical data exemplifies the power of hands-on investigation in unraveling the complexities of magnetic fields. It also serves as a testament to the enduring relevance of classical physics in explaining and harnessing the forces that shape our technological landscape.
Future endeavors could extend this foundational work by exploring magnetic fields in more complex configurations or by integrating advanced computational methods to simulate electromagnetic phenomena, further enriching our understanding and application of magnetic fields in the modern world.
In-Depth Analysis of Magnetic Fields: An Experimental Approach. (2024, Feb 28). Retrieved from https://studymoose.com/document/in-depth-analysis-of-magnetic-fields-an-experimental-approach
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