Solenoid Field Error: Why Highest at Center?

[jmcmillian]

Homework Statement

I ran an experiment to find the magnetic field inside a solenoid at different points using a magnetic sensor, attached to a computer and interface. Starting at the center of the solenoid and moving outwards to the end, I collected points at 1cm increments (starting at the center = 0cm, and then moving outwards to 6cm for each half of the solenoid).

I calculated what the field should be theoretically at each point, and compared it to my findings from the experiment by using basic (%) error analysis.

My experimental values were as much as 16% lower than the theoretical values and as little as 2/3%.

What I noticed was that the error % was the greatest when the sensor was at the center of the solenoid and declined as the sensor was moved towards the end of the solenoid. What I don't understand is if the magnetic field is strongest in the center of the solenoid, why is the error the highest? I would think that a sensor would have an easier time accurately picking up a strong magnetic field as opposed to a weaker field.

Homework Equations

http://www.mountainescapesproperties.com/Magfig4.gif"

The Attempt at a Solution

Distance Experiment B Theo. B Error
(cm) (mT) (mT) (%)
0.000 5.056 6.045 16.36062862
1.000 5.007 5.964 16.04627767
2.000 5.039 5.721 11.92099283
3.000 5.023 5.531 9.184595914
4.000 5.068 4.820 5.145228216
5.000 4.527 4.229 7.046583117
6.000 3.608 3.612 0.09691264
-1.000 5.031 5.964 15.64386318
-2.000 5.023 5.721 12.20066422
-3.000 5.019 5.531 9.256915567
-4.000 5.039 4.820 4.543568465
-5.000 4.600 4.229 8.772759518
-6.000 3.588 3.612 0.650699155

 

[jbsteele]

From the table above, it appears that the error % is highest when the sensor is at the center of the solenoid (0cm). This could be due to a number of factors. One possible explanation is that the magnetic field strength at the center of the solenoid is greater than at other points, making it more difficult for the sensor to accurately measure the field. Additionally, the shape of the solenoid may also play a role, as the shape of the field lines in the center of the solenoid may be more complex than at other points. Finally, the accuracy of the sensor itself may be a factor, as it may not be able to accurately measure fields of varying strengths.

 

[nlightner]

I would first like to commend you on your detailed experimental setup and data analysis. It is clear that you have put a lot of effort into your experiment and have taken appropriate steps to ensure accuracy and reliability.

Now, let's address the issue of the solenoid field error being highest at the center. The first thing to understand is that the theoretical values you have calculated are based on ideal conditions and do not take into account any external factors or imperfections in the solenoid. In reality, there are various factors that can affect the strength and uniformity of the magnetic field inside a solenoid, such as the thickness and material of the solenoid wire, the number of turns, and the presence of any external magnetic fields.

One possible explanation for the higher error at the center of the solenoid could be due to imperfections in the solenoid itself. It is possible that the center of the solenoid has a slightly different wire thickness or a different number of turns compared to the rest of the solenoid, leading to a less uniform magnetic field. This would result in a higher error in measurements taken at the center.

Another factor to consider is the direction of the magnetic field. In your experiment, the sensor was placed perpendicular to the axis of the solenoid, which is the direction of the magnetic field. However, at the center of the solenoid, the magnetic field is not perfectly perpendicular to the sensor, which could also contribute to a higher error.

It is also important to note that the sensor itself may have limitations and errors, especially when measuring strong magnetic fields. It is possible that the sensor may not be able to accurately measure the full strength of the magnetic field at the center of the solenoid, leading to a higher error.

Overall, the higher error at the center of the solenoid can be attributed to various factors such as imperfections in the solenoid, limitations of the sensor, and the direction of the magnetic field. As a scientist, it is important to consider all possible factors and sources of error in an experiment and to continue to refine and improve the experimental setup to minimize these errors.