“Magnetic Fields”
Adam Capriola and Ben York
Performed: March 23, 2010
Report Due and Handed in: March 30, 2010
Purpose
To measure and determine the relationship between a magnetic field generated by a line
of current and a radial distance from a conductor, and to measure and determine the
relationship between a magnetic field at the center of a coil and the number of turns in a
coil.
Hypothesis
As the distance from the center of the conductor increases, the magnetic field strength
will decrease in accordance with the equation B = μoI / 2πR. As the number of turns in
the coil increases, the magnetic field strength will increase, in accordance with the
equation B = NμoI / 2R.
Labeled Diagrams
See attached sheet.
Data
Part 1
Current = 7 A
R (m)
B (mT)
B (T)
1/R (m-1)
0.0050
0.17
0.00017
200.0
0.010
0.12
0.00012
100.0
0.015
0.074
0.000074
66.66
0.020
0.061
0.000061
50.00
0.025
0.044
0.000044
40.00
0.030
0.041
0.000041
33.33
0.035
0.036
0.000036
28.57
0.040
0.031
0.000031
25.00
0.045
0.027
0.000027
22.22
0.050
0.023
0.000023
20.00
0.055
0.019
0.000019
18.18
0.060
0.018
0.000018
16.66
0.065
0.015
0.000015
15.38
0.070
0.013
0.000013
14.28
0.075
0.011
0.000011
13.33
0.080
0.010
0.000010
12.50
0.085
0.0080
0.0000080
11.76
0.090
0.0050
0.0000050
11.11
0.095
0.0030
0.0000030
10.52
0.10
0.0020
0.0000020
10.00
Part 2
Current = 7 A
Diameter of Cylindrical support = 0.130 m
# of turns N
B (mT)
B (T)
1
0.0880
0.0000880
2
0.171
0.000171
3
0.242
0.000242
4
0.312
0.000312
5
0.371
0.000371
6
0.411
0.000411
Graphs
Part 1
Part 2
Questions
Part 1
1. Theory states that the magnetic field produced by a long straight current-carrying wire
decreases in strength as you get further from the wire. The exact dependence of the
magnetic field strength B on radial distance from the wire R is B = μoI / 2πR where μo is
the permeability of free space and has a value of 4π x 10-7 Tm/A. For your data from Part
1, plot a graph in Graphical Analysis of B vs. 1/R. Your graph should have a linear trend.
Perform a Linear Fit on your graph. What is the value of the slope?
The slope is 9.2 x 10-7 Tm.
2. Calculate your value of μoI / 2π. How does it compare to the slope of your graph?
What is the percent difference?
The value is 1.4 x10-6 Tm, which is larger in value in comparison to the slope.
The percent difference is 41%.
Part 2
3. Theory states that the magnetic field produced by a circular loop of current- carrying
wire increases in strength as the number of turns of wire is increased. The exact
dependence of the magnetic field strength B on the number of turns N is B = NμoI/ 2R
where R is the radius of the loop of wire. For your data from Part 2, plot a graph in
Graphical Analysis of B vs. N. Your graph should have a linear trend. Perform a Linear
Fit on your graph. What is the value of the slope?
The graph of the slope is 6.53 x 10-5 T/turn.
4. Calculate your value of μoI / 2R. How does it compare to the slope of your graph?
What is the percent difference?
The value is 6.7 x 10-5 T/turn, which is very similar yet slightly large in value than
the slope. The percent difference is 2.6%.
Conclusion
During part one of the experiment, magnetic field strength was measured as a
function of radial distance from a conductor. First, a piece of polar graph paper with
concentric circles starting at a diameter of 0.5 cm increasing in increments of 0.5 cm to
10 cm was punched through a rigid aluminum conductor at the center of the concentric
circles. The paper was placed on the plastic table of the apparatus and was aligned using
a compass so that the parallel lines on the sheet were pointing north. The paper was then
secured to the apparatus using tape. The high amperage DC power supply was connected
in series with a high power resistor and the aluminum wire at the side and on top of the
apparatus. The magnetic field sensor was zeroed and the DC power supply was set to 7
A. With the current on and kept constant, the magnetic field strength was recorded at
each circle on the polar graph paper by holding the sensor in line with the parallel lines
on the sheet and so that the white dot on the sensor was on the left and at a 90o angle with
the parallel lines pointing north. The magnetic field strength was recorded using Vernier
Lab Pro. This value was recorded along with the respective radius.
Graphical Analysis was used to plot B vs. 1/R and perform a linear trend. The
resulting slope was 9.2 x 10-7 Tm and the correlation was 0.9734. It was somewhat
difficult to get accurate readings at the smaller radii, which negatively affected this
correlation. The slope from this plot in comparison to the value of μoI / 2π, 1.4 x10-6 Tm,
yielded a percent difference of 41%. The data followed the expected trend of decreasing
in magnetic field strength as the radius increased. Possible sources of error include the
difficulty of aligning the sensor perfectly along the radius of each circle, and it was also a
challenge to get an accurate reading from the sensor as the readings kept jumping around.
Additionally, if the sheet was not perfectly aligned northward, there would be
interference from the earth’s magnetic pull which would have affected the readings.
During part two of the experiment, magnetic field strength was measured as a
function of the number of turns in a wire. First, the power supply was turned off and the
center aluminum wire was removed along with the top table of the tangential
galvanometer. The magnetic field sensor was inserted into the side of the cylindrical
support by screwing it into the side of the top table support using a threaded plastic
bushing. The white dot of the sensor was aligned to be in the center of the cylindrical
support with the white dot facing upward. The sensor was zeroed and the power supply
was turn on to 7 A. A piece of flexible wire was wound around the outside of this
support to complete one full turn. The magnetic field sensor measured B using “Events
with Entry” on Lab Pro. The magnetic field strength was measured for six full turns of
the wire. The diameter of the cylindrical support was also measured, being 0.013 m.
Graphical Analysis was used to plot B vs N and perform a linear trend. The
resulting slope was 6.53 x 10-5 T/turn and the correlation was 0.9943. The data followed
the expected trend of increasing in magnetic field strength as the number of turns
increased. The slope from this plot in comparison to the value of μoI / 2R, 6.7 x 10-5
T/turn, yielded a percent difference of only 2.6%. Possible error could have resulted
from the earth’s magnetic field. Additionally, the wire was not perfectly wrapped around
the base, which would throw the readings off as it would not have been an exact turn of
the wire. Finally, it was difficult to align the sensor perfectly in the middle of the
support, so again this would contribute to some error in the readings.
Equations
Percent Difference = |E2 – E1| / [ (E1 + E2) / 2 ] x 100%
B x R = μoI / 2π
B / N = μoI / 2R