Experiment 8
The Determination of
The Strength of the Earth's Magnetic Field
The earth's magnetic field deflects a smafl compass needle in a tangent galvanometer. The current in the coils can be sued to determine the horizontal component of the earth' magnetic field.
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 and requires an angular correction called the magnetic declination angle in order to locate the direction of true north. The field lines also leave and enter the earth's surface at different angles at different positions on the surface of the earth. This angle is called the dip angle. In the Santa Monica area, the magnetic declination angle is 15' east, and the magnetic dip angle is 58 below the horizontal.
The instrument used in this experiment is a tangent galvanometer that consists of circular coils of wire ofiented in a vertical plane. A magnetic field that is parallel to the earth's surface is thus produced, and the magnitude of the field at its center of the coils is
(1)
where o is the permeability of free space, N is the number of tums of wire, I is the current in the
wires, and R is the mean radius of the coils.
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If the coils are oriented so that the field B. due to the coils is perpendicular to the horizontal component of the earth's magnetic field Be , then the net field B is the vector sum of the two fields. From Figure 1, it can be seen that the horizontal component of the earth's magnetic field can be expressed as
(2)
or
(3)
Figure 1. The net magnetic field.
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The horizontal component of the earth's field can now be found knowing 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 0 between 'Be and B. If the compass is first aligned with the magnetic field of the earth and current is supplied to the coils, then the compass needle will undegro an angular deflection aligning itself with the vector sum of the earth's field
and the field due to the coils. This angular deflection is 0.
Apparatus
otangent galvanometer o large vemier calipers
oHeathTri-PowerSupply, ±1% o 2 leads
Procedure
1)Connect channel "A" or "B" output terminals of the power supply to the tangent galvanometer. Choose the connections on the tangent galvanometer that give a convenient number of tums of wire. Record the number of tums.
2)Orient the tangent galvanometer so that the plane of the coils is parallel to the northsouth line as indicated by the compass. The field produced by the coils will then be perpendicular to the earth's field.
3)Tum on the power supply and adjust the current until the compass needle undergoes a deflection of approximately 30'. Record the angular deflection of the compass needle and the current supplied to the tangent galvanometer.
4)Now adjust the current until the deflection is approximately 45. Record the angular deflection and the current.
5)Repeat for a deflection of approximately 60.
Analysis
Use (3) to calculate . the hofizontal component of the earth's magnetic field for the three sets of data and the average of the three values. Express your value in units of Gauss. Report the three values, the average value, the book value for Southem Califomia, and the percentage error between the average value and the book value in a table.
Questions
1)Where is the north magnetic pole located?
2)Begin with the law of Biot-Savart and derive (1).
3)Is there a particular angle 0 at which an uncertainty in the angular deflection causes a minimum uncertainty in the value of the earth's magnetic field?
4)The earth's magnetic field has gone through many reversals during the lifetime of the earth. What do scientists believe to be the possible causes of the reversals?
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