LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
Tangent Galvanometer
Purpose:
To determine the strength of the earth's magnetic field
Equipment:
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Tangent Galvanometer
10 Ω resistor, 6-10 watt
Power Supply
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
(the north geo-magnetic pole) of the earth does not coincide with the north geographic
pole. In fact, the north geo-magnetic pole (where the magnetic field lines emerge) is
located close to the Earth's South Pole, while the geo-magnetic-south Pole is located in
Northern-most 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. In addition to the off-axis nature of the Earth's
magnetic fields, the field lines also leave and enter the earth's surface at an angle (the
magnetic dip angle).
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
at its center of magnitude. 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 (see diagram below, where left right and middle are as viewed from the
front).
left
screw
middle
screw
right screw
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
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
µ0 is the permeability of free space
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.
where:
B
B
e
Bc
Figure l. The net magnetic field B
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.
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
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 5V or 12V terminals of the power supply to the tangent galvanometer.
Choose the terminals that correspond to as many turns as possible. Record the
number of 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.
N
Figure 3. Positioning the Galvanometer
3. Set up the circuit as shown in Figure 2. Use the 10A setting to measure current on the
DMM.
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
4. Set R on the decade resistance box to 50 Ω.
CAUTION: Before taking this step:
NEVER allow a current in excess of 750 mA to flow through the ammeter or power
supply.
If you understand how to prevent the current from exceeding this limit, proceed to
Step 4. If you do not, Ask Your Instructor First!
5. Turn on the power supply
6. Decrease the resistance of the decade resistance box by 5 or 10 ohm increments.
NEVER set the resistance to zero, particularly when changing decades. It is ok to
turn the resistance higher than what you are aiming for and then turn it down again.
Record the angular deflection, θ, of the compass needle and it's uncertainty δθ .
7. 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 by
plotting Bc vs. tanθ, or
µ o NI
2R
vs. tan θ
Eq. 4
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. 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,
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?
3.
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
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
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)?
4. The accepted horizontal component of the earth's magnetic field here in the Bay Area
is:
Be = 2.34 x 10-5 Tesla.
However, 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 = B cos δ.
Eq. 5
Do some research to determine the value of the magnetic field here in the Bay Area.
Also find the inclination angle if possible. From this information and your lab results
determine the experimental value of the inclination angle. Note that there may be a
compass available that allows a rough estimate of the inclination angle.
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 Eqs. 2 and 3.
Results:
Write at least one paragraph describing the following:
• what you expected to learn about the lab (i.e. what was the reason for conducting
the experiment?)
• your results, and what you learned from them
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in
this laboratory.
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
Clean-Up:
Before you can leave the classroom, you must clean up your equipment, and have your
instructor sign below. If you do not turn in this page with your instructor’s signature with
your lab report, you will receive a 5% point reduction on your lab grade. How you divide
clean-up duties between lab members is up to you.
Clean-up involves:
• Completely dismantling the experimental setup
• Removing tape from anything you put tape on
• Drying-off any wet equipment
• Putting away equipment in proper boxes (if applicable)
• Returning equipment to proper cabinets, or to the cart at the front of the room
• Throwing away pieces of string, paper, and other detritus (i.e. your water bottles)
• Shutting down the computer
• Anything else that needs to be done to return the room to its pristine, pre lab form.
I certify that the equipment used by ________________________ has been cleaned up.
(student’s name)
______________________________ , _______________.
(instructor’s name)
(date)
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LPC Physics 2
Tangent Galvanometer
©
2003 Las Positas College, Physics Department Staff
Data Tables
Trial
Resistance
Angular Deflection, θ
1
2
3
4
5
6
7
8
9
10
Best Fit Be: ____________________
Be max: ___________________
Be min: ___________________
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δθ
Current, I
δI