NANYANG TECHNOLOGICAL UNIVERSITY
First Year Engineering Course
FE1073: An Introduction to Engineering and Practices
Laboratory Manual
For
Experiment E2
Magnetic Field
Laboratory : Power and Clean Energy Design
Location: S2-B5c-01
School of Electrical and
Electronics Engineering
[EEE]
1 FE1073-E2
Session 2013/2014
MAGNETIC FIELD
1. OBJECTIVES
When current exists in an infinitely long straight wire, a B field will exist in the region surrounding
the wire. If the current is constant in time, the B field that exists will be constant in time at a given
point. This presence of the constant B field can be detected by a small compass. If the current in the
wire is time-varying, the B field that exists will also be time-varying. This time-varying B field can be
detected by the electric field that it induces in a small inductor coil placed near the wire. In this
laboratory, measurements on an apparatus with a long straight current-carrying wire will be used to
accomplish the following objectives:
1.1 Determination of the direction of the B field surrounding a long straight wire using a compass.
1.2 Confirmation that the direction of the B field near the wire is consistent with the right-hand rule
that relates the current direction to the direction of the B field.
1.3 Determination of the induced voltage in a small inductor coil placed near a long straight wire as
a relative measurement of the B field.
1.4 Demonstration that the magnitude of the B field surrounding a long straight wire decreases with
increasing r, where r is the perpendicular distance from the wire.
1.5 Determination of the induced voltage in a small inductor coil as a function of the ac current in a
long straight wire.
1.6 Determination of the induced voltage in a small inductor coil as a function of the frequency of
the ac current in a long straight wire.
2. EQUIPMENT LIST
2.1 Direct-current power supply
2.2 Sine-wave generator
2.3 Digital voltmeter
2.4 Digital ammeter
2.5 A 100-mH inductor coil (length ≈ 1 cm and inside diameter ≈ 0.5 cm)
2.6 Small compass; long straight wire apparatus. (Consists of a frame on which a continuous strand
of wire is wrapped for 10 loops. The 10 strands are taped together over a length of
approximately 40 cm to approximate a wire whose current is 10 times the current in a single
strand of the wire.)
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3. THEORY
When a current I exists in an infinitely long straight wire, the lines of magnetic induction B are
concentric circles surrounding the wire. At a perpendicular distance r from the wire, the B field is
tangent to the circle as shown in Fig. 1. The direction of the current I is perpendicular to the plane of
the page and directed out of the page. The direction of the current is by definition the direction that
positive charge would flow. The magnitude of the B field as a function of I and r is given by
r
IB
20 (1)
where μ0 = 4 x 10-7
weber/amp-m, I is in amperes, and r is in meters. The units of B are weber/m2,
named as Tesla.
The direction of the B field relative to the current direction is given by following the right-hand rule.
If the thumb of the right hand points in the direction of the current, the four fingers of the right hand
curls in the direction of the B field. It is important to note that the B field forms circles around the
conductor and at each instant they will be pointing in the direction tangent to these circles as shown
in Fig. 1. Also note in Fig. 1 that the length of the B vectors are drawn shorter for the larger circles to
indicate that the B field decreases with distance from the wire as given by equation 1.
Ideally, the above statements apply only to an infinitely long straight wire. In this laboratory the
straight portion of the wire has a finite length L. In order to satisfy the ideal condition, measurements
are made at the center of the wire and within a perpendicular distance of L/4 from the wire.
If the current in the long straight wire is constant in time, the B field created by that current will be
constant in time. Here, the direction of the B field can be determined by observing the effect of the B
field on a small compass placed in the vicinity of the long straight wire.
Fig. 1 B field near a wire carrying current perpendicular to the page and directed out of the page.
If the current in the long straight wire is an alternating current produced by a sine-wave generator, the
B field surrounding the wire will also be time-varying, and it will alternate in direction and magnitude.
If a small inductor coil is placed next to the wire, an alternating voltage will be induced in the coil.
According to Faraday’s law of induction, this induced voltage in the coil is proportional to the rate of
change of the magnetic flux through the coil, and hence to the magnitude of the time-varying B field.
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Therefore, a measurement of the voltage induced in the coil, as the coil is placed at different distances
from the wire, provides a relative measure of the magnitude of the B field at different distances from
the wire. Note carefully that the quantity actually measured is an alternating electric voltage, but its
magnitude is proportional to the B field and will be taken to be a relative measurement of the B field
at a given point.
4. EXPERIMENTAL PROCEDURE – DIRECTION OF THE B FIELD
4.1 Connect the circuit shown in Fig. 2 using the direct-current power supply and the digital
multimeter. Select dc current setting on the multimeter and use the 10A and common sockets for
connection. Arrange the long-wire apparatus so that side A is facing you. Make sure that the
direction of current flow in the bare wire is from top to bottom (Determine the direction of the
current by tracing the wires from the (+) to (-) terminals of the power supply). Have the circuit
checked by your instructor to ensure that the current is in the proper direction before
turning on the power supply.
Fig. 2 Long wire apparatus connected to Direct Current Supply.
4.2 Turn on the power supply and increase the voltage until a current of 2.00A is read on the
multimeter. Do not exceed the current beyond 2.00A.
4.3 Place the compass in the middle of the top horizontal section, directly above the wire and as
close to the wire as possible. State the direction (side A, side B) that the compass needle points.
Record your answer in Data Table 1.
4.4 Place the compass in the middle of the top horizontal section, directly below the wire and as
close to the wire as possible. State the direction (side A, side B) that the compass needle points.
Record your answer in Data Table 1.
4.5 Place the compass next to the bare wire at the four positions indicated by the open circles in Fig.
6 in the Log sheet 1. The represents the downward current viewed from above. In the open
circles representing the four compass positions, draw an arrow showing the direction that the
compass needle points.
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5. EXPERIMENTAL PROCEDURE – B FIELD AS A FUNCTION OF DISTANCE
5.1 Connect the circuit shown in Fig. 3 using the long-wire apparatus and the sine-wave generator.
The detailed connection diagram is given in Fig. 4.
Fig. 3 Long-wire apparatus experimental setup.
5.2 Select ac current on the digital ammeter and connect the ammeter using the 100 mA and
common socket. Select the sine wave and 10 KHz buttons of the sine wave generator. Select ac
voltage on the digital voltmeter. Using the leads that have been twisted about 10 to 15 times,
connect them between the voltage and common sockets to the inductor coil of 100 mH self-
inductance. This is extremely important because it will minimize the voltage induced in the
leads themselves and ensure that the voltage induced is in the inductor coil. The inductor coil is
placed on the platform as shown in Fig. 5. The axis of the inductor coil is perpendicular to an
imaginary line (shown as the dotted line labeled I in Fig. 5), which is in turn perpendicular to the
current-carrying wire. The inductor coil was shown in three different positions with the axis of
the coil at different distances r1, r2, and r3 from the wire. At each position of the inductor coil
shown, the B field will alternate in opposite directions along the axis of the coil. The coil is
chosen to be short (≈ 1 cm) and of small cross section (diameter ≈ 0.5 cm) because for that
choice, the B field lies approximately along the coil axis and is approximately uniform over the
cross section of the coil.
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Fig. 4 Long wire apparatus connection diagram.
Fig. 5 View of the platform looking down from above. The current is perpendicular to the page
alternating into and out of the page.
5.3 The amplitude of the induced voltage on the digital voltmeter will depend on the frequency of
the sine-wave generator. With the inductor about 3 cm from the wire, and its axis positioned as
shown in Fig. 5, turn the sine-wave generator to its maximum output amplitude by turning the
amplitude knob fully clockwise. Vary the frequency of the generator by tuning the frequency
dial until a maximum voltage is read on the digital voltmeter. Record the frequency in Data
Table 2. Once this frequency is found, do not change the frequency. Make all measurements at
this frequency.
5.4 Measure the voltage induced in the inductor coil as a function of r (Fig. 5). The quantity r is the
distance from the center of the coil ( indicated by the white marker ) to the center of the wire.
Take data from r = 3.0 cm to r = 9.0 cm, in increments of 1 cm. Since the B field is extremely
nonuniform over the coil cross section close to the wire, data is not taken for r less than 3 cm.
Record the values of the voltage in Data Table 2 under the column labeled V. If this were a true
measure of the B field, the units would be in Tesla. Since the measured quantity is voltage, the
units are in volt.
6. EXPERIMENTAL PROCEDURE – B FIELD AS A FUNCTION OF FREQUENCY
6.1 Use the same circuit as in the above section.
6.2 Move the inductor to a distance of 3 cm from the long wire (r = 3 cm).
6.3 Select the 1 KHz button and set the output current from the sine wave generator to 40mA.
6 FE1073-E2
6.4 Vary the frequency of the sine wave from f = 5 kHz to 12 kHz at 1 kHz steps and record the
voltmeter reading in Data Table 3. For each set of reading make sure the current is maintained at
40mA. The current can be adjusted by turning the amplitude knob of the sine wave generator.
7. EXPERIMENTAL PROCEDURE – B FIELD AS A FUNCTION OF CURRENT
7.1 Use the same circuit as in the above section.
7.2 Move the inductor to a distance of 3 cm from the long wire (r = 3 cm).
7.3 Set the frequency of the sine wave generator to 70 kHz.
7.4 Vary the current in the wire by turning the amplitude knob of the sine wave generator from 10
mA to 45 mA in steps of 5 mA.
7.5 Record the voltmeter reading for each current setting in Data Table 4.
8. GRAPHS
8.1 Use the data in Data Table 2 draw a graph of induced voltage V versus 1/r.
8.2 Use the data in Data Table 3 draw a graph of induced voltage V versus frequency f.
8.3 Use the data in Data Table 4 draw a graph of induced voltage V versus current I.
9. FORMAL REPORT
9.1 Derive an expression for the magnetic field B at a point of distance r, from an infinitely long
wire that carries a current I. Your derivation should include the direction of the magnetic field
with respect to the direction of current flow. Verify your expression by using the experimental
results obtained. If your results do not show the expected relationship, explain why.
9.2 Derive and comment on the dependence of the induced voltage in the inductor coil on the (i)
frequency and (ii) magnitude of the ac current flowing in the long wire. Verify your answers by
using the experimental results obtained. If your results do not show the expected relationships,
explain why.
The report length should not be more than 15 pages.
10. REFERENCES
[1] R. A. Serway & R. J. Beichner, 2004, “Physics for Scientists and Engineers with Modern
Physics”, 6th Edition, Saunders College Publishing.
[2] E. R. Jones & R. L. Childers, 2000, “Contemporary College Physics”, McGraw Hill.
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Experiment E2: Magnetic Field
DATA SHEET 1
Name : ______________________________________ Date : ______________
Group : ______________________________________
Data Table 1
With compass above wire, compass direction =
With compass below wire, compass direction =
Fig. 6 Indicate the compass direction at the positions shown.
Sine wave amplitude = maximum r = 3cm, I = 40mA r =3 cm,
Freq. = 70 KHz
Data Table 2 Data Table 3 Data Table 4
r
(cm)
1/r
(cm-1
)
V
(volt)
f
(KHz)
V
(mvolt)
I
(mA)
V
(volt)
3.00 5 10
4.00 6 15
5.00 7 20
6.00 8 25
7.00 9 30
8.00 10 35
9.00 11 40
12 45
Frequency of ac current: ________
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DATA SHEET 2
9 FE1073-E2
DATA SHEET 3
10 FE1073-E2
DATA SHEET 4
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DATA SHEET 5
QUESTIONS
1. Are your answers to the questions in Data Table 1 about the direction in which the compass
needle points consistent with the right-hand rule for the direction of the B field?
2. State the extent to which your measurements confirm the expectation that B field is proportional
to 1/r for the long wire.
12 FE1073-E2
DATA SHEET 6
3. When the direct current is 2.00 A in a single wire of the bundle of 10 wires, the total current in
the bundle of wire that approximates the long straight wire is 20.0 A. What is the magnitude of
the B field 3.00 cm from this long straight wire carrying a current of 20.0 A? What is the
magnitude of the B field 9.00 cm from the wire carrying 20.0 A?
4. A constant current flows in a long straight wire in the plane of the paper in direction shown below
by the arrow. Point X is in the plane of the paper above the wire, and point Y is in the plane of the
paper below the wire. What is the direction of the B field at point X ? What is the direction of
the B field at point Y ?
X
Y
Direction at X = _________________________
Direction at Y = _________________________
13 FE1073-E2
DATA SHEET 7
5. Based on the experimental results obtained, comment on the relationship between the induced
voltage V in the inductor coil and the frequency f of the ac current flowing in the wire.
6. Based on the experimental results obtained, comment on the relationship between the induced
voltage V in the inductor coil and the magnitude of the ac current I flowing in the wire.
14 FE1073-E2
APPENDIX 1
Additional Theory
Assuming an infinite wire, the magnetic flux density B at a distance r from a wire of M turns is
r
MIB
20
0 (A1)
where I is the current flowing in the wire
Assuming that the inductor has N turns and has r as its
core. The magnetic flux density B in the core of the inductor is
r
MIBB r
r
20
0 (A2)
The magnetic flux through the inductor is
NAB (A3)
where A is the cross-sectional area of the inductor.
r
IMANr
20 (A4)
The inductance L of the inductor is given by
l
ANL r
20
(A5)
where l is the length of the inductor.
From (A4) and (A5),
Nr
lLMI
2 (A6)
The induced voltage in the inductor due to a changing is given by
dt
dE
(A7)
