LPC Physics
Tangent Galvanometer
Revised 12/08
Tangent Galvanometer
Purpose:
To determine the strength of the earth's magnetic field
Equipment:
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Tangent Galvanometer
6V Lantern Battery
Patch Cords, Alligator Clips
Ruler, Meter stick
DMM
Decade Resistance Box
Magnetic Compasses
Theory:
The magnetic field of the earth is thought to be caused by convection currents in the outer
core of the earth working in concert with the rotation of the earth. The field has a shape
very similar to the field produced by a bar magnet. However, the north magnetic pole of
the earth does not coincide with the north geographic pole. In fact, the north geomagnetic pole (where the magnetic field lines emerge from the Earth’s surface) is located
close to the Earth's South Pole, while the geo-magnetic-south Pole is located in Northernmost Canada. Since the North Pole of a compass points towards the Earth's geomagnetic
south pole, the determination of "true North" requires an angular correction known as the
magnetic declination. The field lines also leave and enter the earth's surface at an angle
(the magnetic dip angle).
Equipment and theory
The instrument used in this experiment is a tangent galvanometer that consists of fifteen
turns of wire oriented in a vertical plane that produce a horizontal magnetic field. The
fifteen coils are actually two sets of oppositely directed coils, with five turns coiling
counterclockwise when viewed from the front and ten coiling clockwise.
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LPC Physics
Tangent Galvanometer
Revised 12/08
From the Biot-Savart law, the magnetic field at the center of the coil due only to the
current I is given by:
Bc =
µ o NI
Eq. 1
2R
µο is the permeability of free space
where:
N is the number of turns of wire
I is the current in the wires
R is the mean radius of the coils.
Note that this field vector is perpendicular to the plane of the coil.
If the coils of the galvanometer are oriented so that the Earth's magnetic field (Be)
is parallel to the plane of the coils, and the magnetic field due to the current (Be) is
perpendicular to the coils (as shown below) the net field B is the vector sum of the two.
B
B
e
Bc
Figure l. The net magnetic field, B
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LPC Physics
Tangent Galvanometer
Revised 12/08
From Figure 1, it can be seen that the horizontal component of the earth's magnetic field
Be can be expressed as
tan θ =
Bc
Be
Eq. 2
where θ is the compass reading. Note that Eq. 2 can be rearranged to allow a linear
relationship between Bc and tanθ
µ o NI
2R
= Be tan θ
Eq. 3
The horizontal component of the earth's field can now be found by measuring the field
due to the coils and the direction of the net magnetic field relative to the direction of the
earth's field.
Because a compass aligns itself with the lines of force of the magnetic field within which
it is placed, a compass can be used to find the angle θ between Be and B. If the compass
is first aligned with the magnetic field Be and current is then supplied to the coils, the
compass needle will undergo an angular deflection. This angular deflection is θ.
Experiment:
1. Connect the battery to the tangent galvanometer. Use the left and middle screws so
that the coil consists of ten turns.
R
Power
Supply
A
Tangent
Galvanometer
Figure 2. The net magnetic field B
2. Orient the tangent galvanometer so that the plane of the coils is parallel to the northsouth line as indicated by the compass without the applied field (see Figure 3.). The
field produced by the coils will then be perpendicular to the earth's field.
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LPC Physics
Tangent Galvanometer
Revised 12/08
N
Figure 3. Positioning the Galvanometer
3.
Set R on the decade resistance box to 50 Ω.
4. Decrease the resistance of the decade resistance box by 5- or 10-ohm increments.
Record the angular deflection θ of the compass needle and it's uncertainty δθ .
5. Record the current I and its uncertainty δ I. Record at least 10 values.
Analysis:
1. Use Eq. 3 to calculate the horizontal component of the earth's magnetic field for each
angle. To do this you use Eq. 3 and plot Bc vs. tanθ, or
µ o NI
vs. tan θ
2R
so that Be will be the slope of your plot. Display your results graphically and
determine Be from the your "best fit" straight line.
2. Unless you are extremely lucky, your results will not agree exactly with the accepted
value (see below). As with most labs, however, your values need only agree within
the experimental uncertainty. Using the techniques of error analysis, the uncertainty
in Be using Eqs. 1 and 2 is given by:
⎛ ∆I
∆R
∆θ
∆Be = Be ⎜⎜
+
+
R
sin θ cos θ
⎝ I
⎞
⎟
⎟
⎠
Eq. 4
where ∆θ is in radians.
3. In this experiment, however, you are not calculating Be directly from a single
equation, and one set of independent variables. Instead, you are performing a "best
fit" from several data points. This implies that the best method for determining ∆Be is
to determine the maximum and minimum slopes that fit your data points. In doing so,
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LPC Physics
Tangent Galvanometer
Revised 12/08
be sure to include the uncertainties in the current and angle in creating your new
ranges (i.e. graph Bc(I+∆I) vs. tan (θ+∆θ). Determine the values of Be max and Be
min that are consistent with your data. Does the accepted value fall within this range?
4. Is there a particular angle θ at which you could suggest making measurements so as
to minimize the angular uncertainty? Explain. Before you take the equipment apart,
change the current until this angle is reached. Use Eq. 2 to determine the value of Be
using this angle and current (if you don't already have this value in your data table).
How does this value compare with the value you obtained in Step 2?
5. The Earth's magnetic field does not actually pass horizontally through the coils.
Instead it comes in at an inclination angle, δ, so that
Be = Bcosδ.
The local field strength, declination, and inclination can all be found at:
http://www.ngdc.noaa.gov/seg/geomag/jsp/IGRFWMM.jsp
Supplemental Questions (to be turned in with your lab report)
1. Where is the north magnetic pole of the earth located?
2. What is the magnetic declination?
3. What is the magnetic declination in the bay area?
4. Begin with the Biot-Savart Law and derive Eq. 1.
5. Derive Eq. 4 from Eq. 2 and 3.
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Eq. 5