Download Physics 121 Lab 4 - Earth`s Magnetic Field 1 Theory

Physics 121 Lab 4 - Earth’s Magnetic Field
1
Theory
The Earth’s magnetic field is well known and heavily studied. It also is ever present and
affects any experiments in which relatively small magnetic fields are involved. In this lab, we
will use our knowledge of the magnetic field created by currents to measure the strength of
the horizontal component of the earth’s magnetic field. We will use a simple device called a
tangent galvanometer, which consists of a small magnetic compass at the center of a circular
coil of wire. A power supply provides an electric current that produces a magnetic field at
the center of the coil where the compass is located. The B field of the current is directed
perpendicular to the plane of the coil.
What is the formula for B at the center of a current loop?
The horizontal component of the Earth’s field, BEH , tries to align a compass needle toward
magnetic north. If the plane of a current-carrying coil is aligned parallel to BEH , the field
of the coil Bcoil will be perpendicular to the direction of BEH , i.e., it will act along the
east-west direction. The net magnetic field acting on the compass needle is then the sum of
the two perpendicular vectors, BEH and Bcoil , determining the resultant orientation of the
needle. The angle θ, shown in Figure 1, through which the needle is deflected away from the
direction of BEH gives a measure of the strength of the field Bcoil relative to the strength of
the horizontal component of the earth’s magnetic field BEH .
BEH
θ
Bcoil
Figure 1: The deflection of the compass needle due to the magnetic field of the coil perpendicular to the horizontal component of the earth’s magnetic field.
Write the relationship between Bcoil , BEH and θ.
Figure 2: Setup to measure the Earth’s magnetic field
2
Setup
The tangent galvanometer consists of a circular coil of wire of N turns, a power supply to
provide the current to the coil, and a small magnetic compass placed at the center of the coil
to measure the resulting electric field. Follow the directions below to set up the experiment,
referring to Figure 2.
a) Measure and record the radius, R, of the coil with uncertainty.
b) Record the number of turns of wire, N, as given on the coil label.
c) Check the polarity of your compass away from other magnetic fields (magnets, electronics).
d) In addition to the coil, power supply, and compass, you will use a 220 Ω resistor and
a multimeter to measure the current. Set the multimeter to mA input. Connect the
components of the circuit, as shown in Figure 2. Connect the ’+’ socket of the power
supply to the leftmost socket in the coil housing. Connect the middle socket in the coil
housing to a socket in the resistor. Connect the other socket of the reister to the µmA
socket of the multimeter (not the 10A socket!). Finally, connect the ’Com’ socket to the
’-’ socket in the supply. IMPORTANT: do NOT turn on the power until your
instructor has checked your circuit (or you can blow a fuse in the meter).
Based on the way the coil is wired, which way will the magnetic field point (draw a
picture)? Note that the conventional current flows out from the + terminal to the terminal of the power supply, and the electron current flows in the opposite direction.
e) Place the compass at the center of the crosshair on the platform of the coil making sure
that the N axis of the compass is aligned perpendicular to the axis of the coil (rotate
the coil until this is the case). Monitor the placement of the compass throughout the
experiment, making sure the center of the needle is centered on the crosshair and that
the north direction is along the long axis of the crosshair.
f) Carefully rotate the compass and coil until the ends of the compass needle are aligned
with 0◦ and 180◦ on the compass scale.
g) HAVE YOUR INSTRUCTOR CHECK YOUR CIRCUIT.
3
Procedure
3.1
Preliminary measurements
a) Try running a current through the circuit to see that the compass needle does indeed
deflect: watch the compass needle as you slowly turn up the voltage on the power supply.
Is the direction of the deflection consistent with your prediction in the Setup section? If
not, make sure your circuit is set up as instructed and check the compass polarity. If
necessary, revist your prediction.
b) Now do things more carefully. Turn on the power supply and set the current so that
the compass deflects through 40◦ . Turn off the current, and perform the measurement
again to make sure it is repeatable. Any difference is a measure of your uncertainty.
Monitor both sides of the compass needle in case the angle is different. If the angles are
different, record both angles. Discuss with your partner the best way to measure the
angle accurately and how to estimate the uncertainty in the angle measurement. Record
your angle(s) and current with uncertainties.
c) Turn off the power supply, reverse the leads and repeat the last step. If necessary, adjust
the current to get to the same angle. This is another source of uncertainty. Record your
new current and uncertainty.
3.2
Data Collection
We will make 4 additional measurements using different angles and currents to get a better
estimate of the Earth’s magnetic field. Make your own spreadsheet to contain your data.
a) Use your adopted method of current and angle measurement from the previous section.
b) Measure and record the current(s) needed to deflect the needle to a new angle. Record
your angle(s) with uncertainty.
c) Reverse the leads and record the current(s) to get to the same angle.
d) Repeat steps a) and b) to get a total of 5 trials, including your inital set of measurements
(make sure to alternate the leads between each measurement).
e) Record each measurement and its uncertainty in your data table.
4
Data Analysis
Devise a graphical method to determine BEH , based on the relationship you derived between
Bcoil , θ, and BEH and the data you collected.
Apply your procedure to determine the Earth’s magnetic field. Be sure to include uncertainty
in your answer.
How does your answer compare to the known local magnetic field? Google ‘NOAA Magnetic
Field Calculator’ and enter Schenectady’s zip code to get a estimate. Be sure to include the
uncertainty for comparison to your result and reference your source in your report.
For your report, turn in an Abstract and a Results section.