# Lab 08 Magnetic Fields

### Resources

• Video demonstration
• Accompanying Capstone file
• The video mentions an online manual, but this has become obsolete due to changes in the lab forced by distance learning. There seems little point in having you buy an obsolete manual.
• Capstone Software is required to access the data in the file. There are versions for IOS and windows. THere is a capstone file with the data in the Blackboard assignment.

### Introduction

A current in a wire, generates a magnetic field, B, concentric with the wire,in a direction defined by a right-hand rule, which you should know by now. Loop that wire into a coil and stack many of those coils and you have a solenoid, inside of which the magnetic field adds through the magic of the superposition principle. The magnitude of the field inside an ideal solenoid is given by

Where = 1.26e-6H/m is the permeability, n is turn density (turns per length) and I is the current.

Unfortunately, an ideal solenoid is infinitely long, or at the very least, length >> radius, and such devices are not available to us. The dimensions of the coils we’re using can be read from the photos on the ‘Equipment’ page. The field in coils, for which the radius is of the same order as the length, can be adjusted using the following correction.

where a is the radius of the coil and l its length. Since you may not know how to read the calipers I’ll give the values here, a = 2.060cm, l = 4.025cm.This is the model you will be exploring.

### The Report

#### ●      Abstract

• The magnetic field due to a current carrying wire, a feature of all undergrad programs and is the historical path to Electromagnetism. Briefly discuss its importance in day to day life.

#### ●      Data

• All data should be tabulated in the report.

#### ●      Analysis

• Any plots or calculations should be shown in the report. If your doing multiple calculations of the same type do one as a sample.

#### ●      Conclusion

• Discuss how your results support the model and respond to specific requirements in the Conclusion section.

### Procedure 1

Magnetic Field strength, B for increasing number of turns, N.

#### ●      Data

• The capstone file, under the procedure 1 tab, has 4 runs in which the magnetic field strength has been measured for coils of 200, 400, 800, 1600 turns. The video demonstrates how the data was collected and how to extract the peak field.
• Plot B vs N in Excel
• The data can be accessed on the ‘Procedure 1’ page using the ‘Select Visible Data’ tool.

#### ●      Analysis

• Add a best fit line (a trendline in Excel) to your plot. Be sure to add the equation and r value.
• Should the intercept be set to 0 for this fit?
• Does the data support the model?
• What does the slope represent here?
• Find a value for μ0 from your data and compare, percent error, it to the constant given in the introduction.

### Procedure 2

Magnetic Field strength, B for increasing current, I.

#### ●      Data

• The data collected models another configuration of the variables. Each run measures the magnetic field strength with fixed n and varying current.
• Find the slope for each run using a best fit in Capstone.
• You can see the data on the ‘Procedure 2’ once again using the ‘Select Visible Data’ tool.

#### ●      Analysis

• Does the data support the model?
• For each run calculate the value of μ0 from the slope and other factors.
• Do these values match the value found in the first procedure?
• Average your 5 values of μ0 and compare it to the value given in the introduction.

### Conclusions

The value of μ0 is well known, and our effort here is just a way to test the model we’re examining. Discuss how the percent difference you found reflects on this lab.

It’s easy to ignore a small experimental error in a lab like this, however, if your values are all consistently lower than the known values and by similar amounts, it suggests the possibility of a systematic error in our experiment and that means it’s possible to correct it. Discuss this possibility and suggest possible sources of the error.

One thing you might question is the correction factor we used for coils of finite length. Calculate the percent error between the formula for an infinite coil and a coil of fixed length. This is one of the times when you should do the algebra first before getting your calculator involved. The chance to simplify through cancelations is a rare gift.