Physics 4BL LAB 3: Magnetism

Partners:

Enrique A. Segura

Venudhar Ravinshankar.

Date: May 28th, 2014

Introduction

In the following report we will address Faraday’s Law by measuring magnetic fields and also induced voltages in coils. Using a Hall probe, data is obtained to show the relationship between magnetic field intensity and radial distance. In doing this report we will use correlation data obtain through data analysis, linear regression. That coefficient will be address the data obtain experimentally versus the expected results from theory. This value, R squared, is meaningful, as its value is close to one, its correlation has a lesser degree of error.

Experimental Results

We conducted tests to assess the independence of the magnetic field regarding orientation (in terms of the field; not of the Hall probe, as you will see before). Through experiments it is observed that as distance is increased, between the source and the test object, the field weakens. Moreover, it also mattered the orientation of the probe. If you have the probe flipped, the measurements will give a negative magnitude, thus, showing the cross product we know from theory. In this graph, the data for this experiment is recorded and showed.

Graph 1: Magnetic Field (in T) vs Radial Distance (m) for the First Experiment.

0 0.02 0.04 0.06 0.08 0.1 0.120

0.00005

0.0001

0.00015

0.0002

0.00025

Magnetic Field vs Radial Distance

Series2

Distance (m)

Fiel

d (T

)

As you can see in the graph, it is not linear. If you notice at a specific field strength level in the y-axis, there are several points in in the x-axis. And also, as distance is increase the data points range (several points at a field strength) is decreased. This is consistent with the data we obtained, which also stands with the theoretical expectations.

Moreover, there is an inquiry that needed some experiment work, for its importance: the behavior of magnetic fields in between permanent magnets as orientation of the magnet is changed with respect with the other. From theory we know that there is a cross product involved with means the orientation, in form of an angle, is involved. The data was obtained at both parallel, 0 degrees, and at 90 degrees.

Graph 2: Permanent Magnet Interaction (in T) vs distance at 90 Degrees.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

Permanent Magnetic Interaction at 90 Degrees

Series2

Distance (m)

Mag

netic

Fie

ld (T

)

Graph 3: Permanent Magnet Interaction (in T) vs distance at 0 Degrees.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

Magnetic Strength at 0 degrees

Series2

Distance (m)

Mag

netic

Fie

ld (T

)

It is important to see that the behavior of the magnetic field in between the two mirrors each other, which reinforces the idea that magnetic field does not change, its physical characteristics, with the minor exception of magnitude. And that is importance, the question of

magnitude. Magnitude does change when the magnets at perpendicular relative to each other. The difference amounts to a factor of two from the parallel measurement to the perpendicular orientation. In regards with vector direction, if the measurement is negative, it shows that the probe position, respect with the field, is out of phase (flipped).

Theory gives us the following: there is a force due to magnetic fields. By means of a digital balance, the mass reading of said balance can be used to obtain the force between two permanent magnets and show the relation between force and the magnetic field as distance changes. The following graph shows that.

Graph 4: Magnetic Force (in N) vs Distance Ratio (1/m) between Permanent Magnets.

10 15 20 25 30 35 40 45 500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Magnetic Force vs Distance Ratio

Series2

DIstance Ratio (1/m)

Mag

netic

For

ce (N

)

Let me clarify the ratio, and why is it used instead of just distance instead of the shown 1/ distance. The issue is that with the ratio it is clear the relation from theory and it correlates with our data so far as to show that at the closest range between the magnets the force is strongest. If you use only distance you get the reverse of this graph and it is harder to visualize that way. This graph reinforces the idea that we have seen before, and backed by data obtained, that proximity relates to field strength, and by extension, its force, and provided there is no angle in between the magnets, the obtained measure is the highest.

Now, let us move forward to Faraday’s Law. We know that a changing magnetic field, from theory, if taken the rate of change of the magnetic field, creates an induced emf, or in this case, induced voltage. Moreover, let us also include Lenz’s law, which address the vector

direction of said emf, and moreover, it can also, tell us the direction of the field. The following graph shows the relation between voltages versus time in this scenario.

Graph 5: Induced Voltage vs Time

0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02

-1.00E-02

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

Induced Voltage vs Time

Time (s)

Volta

ge (V

)

In this graph, the amplitude of the sinusoidal wave, which is the induced voltage, is around 1.88exp(-3).

And in this graph, the same process is done to the data obtained to show the induced current.

Graph 6: Induced Current vs Time.

0.00E+00 2.00E-03 4.00E-03 6.00E-03 8.00E-03 1.00E-02 1.20E-02

-5.00E-03

-4.00E-03

-3.00E-03

-2.00E-03

-1.00E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

Induced Current vs Time

Time (s)

Curr

ent (

A)

In this graph, by the same logic, the induced current is around 4 exp(-3) amperes.

Analysis

We want to show the behavior of magnetic fields due to distance ratio in an approximation of a line a charge.

Graph 7: Radio Distance vs Magnetic Field

0 10 20 30 40 50 60 70 800

0.00005

0.0001

0.00015

0.0002

0.00025

Ratio Distance vs Magnetic Field

Magnetic Field (T)

Ratio

Dist

ance

(1/m

)

When implemented linear regression, this is the data obtained:

Summary Output:

Regression Statistics

Multiple R0.70288456

2

R Square0.49404670

8Adjusted R Square

0.465938192

Standard Error4.23659E-

05Observations 20

ANOVA df SS MS

Regression 1 3.15474E-08 3.15E-08Residual 18 3.23076E-08 1.79E-09Total 19 6.3855E-08

CoefficientsStandard

Error t Stat

Intercept 6.2974E-05 1.68708E-053.73272

7

X Variable 12.67143E-

06 6.37204E-074.19242

3

The correlation factor is the one on the second row of the table. While statistically speaking is not promising as it is lower than half of the 1, which is shows how close and error free the data is. However, from a physical standpoint, I will argue that the experimental data shows that experiments do show promise and accuracy.

Graph 8: Distance Ratio vs Magnetic Field at Parallel (0 degrees)

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.00060

1000000

2000000

3000000

4000000

5000000

6000000

7000000

8000000

9000000

Distance Ratio vs Magnetic Field at 0 Degrees

Series2

Magnetic Field

Dist

ance

Rati

o

And here is the summary output for regression:

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.503081R Square 0.253091Adjusted R Square 0.226415Standard Error 0.000126Observations 30

ANOVA df SS MS F

Regression 1 1.5E-07 1.5E-079.48781

1

Residual 28 4.42E-071.58E-

08Total 29 5.92E-07

Coefficient

sStandard

Error t Stat P-value

Intercept 0.000136 2.35E-055.78008

93.31E-

06

X Variable 1 4.92E-11 1.6E-113.08022

90.00460

2

Graph 9: Dipole Interaction Magnetic Field vs Distance Ratio.

10 15 20 25 30 35 40 45 500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Magnetic Field vs Distance Ratio

Ratio Distance

Mag

netic

Fie

ld(T

)

And here is the linear regression data:

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.610031R Square 0.372138Adjusted R Square 0.351209Standard Error 0.059006Observations 32

ANOVA df SS MS F

Regression 1 0.0619080.06190

817.7812

2

Residual 30 0.104450.00348

2Total 31 0.166359

Coefficien

tsStandard

Error t Stat P-value

Intercept 0.150914 0.0277715.43426

96.84E-

06

X Variable 1 -0.00449 0.001065-

4.21678 0.00021

I have to admit that the R square correlation factor is too low means that this data does not fit well, speaking statistically. However, please take note of the graphs, as they do contemplate the behavior expected from theory.

Conclusion

As for the statistics, I am sad to report that it did not work out; my results do not fit well. So in that account, my data analysis does not aid the case for Faraday’s law. However, looking at data, we can see trends that helps see the physics behind the experiment. And in those accounts, we have meet the goal of showing the validity of experiments.