LabMFS - Magnetic Field in a Solenoid
Objective Statement
To investigate whetherthe magnetic field inside a solenoid is affected by the current through the solenoid and how the magnetic field depends on it.
Data
I (A)
B (Gauss)
1.00
1.1
2.00
3.4
3.00
5.5
4.00
7.5
5.00
10.0
The length ofthe slinky is 4.00inches and the number of turns is 20.
Derivations
In the ideal case, by using Ampere’s Law, we have . Then we getthat , where is the magnetic constant, the number of turns, and the length of the slinky. Using the data we get from our experiment, we can test the above equation. We are going to obtain the slope by analyze our data and compare it with the one acquired from the theoretical equation.
Method and Setup
ቤተ መጻሕፍቲ ባይዱWe assume that the magnetic field inside a solenoid are related to the current.
•We connect a slinky to a power supply in series with amultimeter. Fix the slinky and place the sensor of aGaussmeterat the center of the slinky. Make surethe large side of the sensor is parallel to the cross section of the slinky.
Error Discussion
Since the coefficient of the regression line is close to 1,we could say that the linear correlation between the current and the magnetic field is statistically significant. We could find the theoretic value of the slope is great than our measurement.It may be the result of using idealizations when deriving the theoretic equation. In theory, we suppose that the solenoid is infinitely long. But this assumption is not true in practice. So the actual measurement of the magnetic field is a little bit less than ourprediction.
•Turn on the power supply e the current control knobs to adjust thecurrent through the slinky to 1.00A, 2.00A, 3.00A, 4.00A, and 5.00A successively and record themultimeterreadings respectively.
•Draw a scatter plot with the data.X-axis is stand for magnitude of the current and Y-axis is stand for magnitude of the magnetic field. Use statistical methods to infer the relationship between thecurrent and the magnetic field according to the distribution of pointson the plot.
Graphs
Calculations
Since ,the theoretical value of the slopeis .And the slope obtained from the data is .
Objective Discussion
From the scatter plot, it is easy to observe a linear correlation between the current and the magnetic field. Using statistical analysis, weget , sowe could safely draw the conclusion that themagnetic fieldinside a solenoid linearly depends onthecurrent through the solenoidif other factors arefixed, which is consistent with the classic theory.