MAGNETIC INDUCTION FIELD OF THE EARTH
The earth posss a magnetic field, as anyone who has ud a compass knows. Although the existence of the field is no doubt related to the prence of ferromagnetic iron in the earth's core, the mechanism by which the field aris is imperfectly understood. The symmetry of the field is similar to that of a bar magnet or to the field generated by current flowing in a circular coil. the object of this experiment is to measure the magnitude the direction of the earth's field at one station in the laboratory. The device ud is called a rotating coil magnetometer and is bad on the principle of electromagnetic induction.
Theory and Apparatus
Definitions
By definition, the direction of a magnetic induction field, B, is the direction in which the north pole of a freely-suspended compass needle points when at rest in the field. Thus B is a vector quantity. The magnitude or strength of the field is defined in terms of the force which the field exerts on a charged particle moving in it. This definition, however, is rather awkward to apply in actual measurements of B. In this experiment, B will be obtained from a measurement of the emf induced in a rotating coil.
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From experiments with magnetic compass and magnetometers, the large scale symmetry of the earth's field is known to remble the sketch below in Fig. 1.
At some arbitrary location on the earth's surface B has both a horizontal and a vertical component as shown in Fig. 2. The angle % which B makes with the horizontal is called the angle of dip. At any point on the equator the field is horizontal (i.e., B v = 0). At the poles it is vertical (i.e., B h = 0).
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The Magnetometer and Principles of Operation
Magnetic field will be measured with a device called a rotating coil magnetometer. Examine the instrument and identify the two large Helmholtz coils - coils C - and the smaller,
centrally-located arch coil - coil S. Coil S is rotatable, being attached to a shaft.
Fig. 1 Symmetry of earth's
Fig. 2 Angle of dip of earth's magnetic field.
magnetic field.下火水果
driven by a small electric motor. The magnetometer you are supplied with is only for student u,having much larger dimensions than the ones manufactured commercially, but the principles are the same.When a coil of wire, say coil S, is placed in a magnetic field of strength B, say the earth's field, an emf can be induced in the coil by changing the flux through the coil. If i B is the magnetic flux through the coil, Faraday's law gives the induced emf as
,dt
d - = B Æ
e The flux can be changed in a number o
f different ways. Two are of interest to us:
1.by varying the magnetic induction, B, with time, when the coil is held stationary, and
2.by rotating the coil about an appropriate axis when the field is constant.
Method 1 is employed in the experiment, "Magnetic Induction Field of a Circular Coil". Method 2
is ud here.
3Let Fig. 3 on the next page reprent coil S. Suppo B is perpendicular to the axis of rotation, and at an angle q with respect to the normal to the plane of the coil. Then by
definition, the magnetic flux through the coil is given
by the area of the coil and B is the absolute value of
滚球比赛
the field strength. For a coil with n turns of wire,
,
cos nBa = B q ÆFig. 3 The Rotating Coil.
If the motor rotates the coil at an angular velocity/frequency of ω rad c.-1, then θ = ωt and from eq
s (1) and (2),t
sin =t sin naB = (t)o w e w w e This emf, appearing across the terminals labelled `rotating coil' on the magnetometer, can be measured. It is large enough not to require amplification.
Note that the apparatus can be laid flat or tipped up on end. This enables the arch coil to be rotated about either a horizontal or a vertical axis - and hence sample either B v or B h .Peak-to-Peak and RMS Detection
焦灼的心For the most part, the emf will be measured with the multimeter. But an oscilloscope can also be ud. When the oscilloscope is ud, peak-to-peak (pp) values are obtained as shown
below in Fig. 4. The multimeter, however,
displays a root-mean-square (rms) value. This
is becau when an AC voltage is applied to
the multimeter t to the AC volts
mode the signal is first rectified and then
filtered. The result is a DC voltage equal to
the root-mean-square of the AC input.
Fig. 4 Relationship between sinusoidal
signal and its DC root-mean-square.
4That is,
e e pp
rms 221
= and
,
22 = 2 = rms o pp e e e The Oscilloscope - An Introduction
Fig. 4 shows a front view of the Philips model PM3232 oscilloscope ud in this experiment. It is a dual beam device, but you will u only one beam - beam B. As can be en from the figure there are too many controls for each one of them to be discusd parately here.
Fig. 5
Front view of Philips oscilloscope
The following familiarization routine is intended only for tho students who have not ud a scope before and is designed to yield a Lissajous figure - a necessary condition for measuring frequency in this experiment.
Before switching on, carry out the following checks:
1.
intensity control mid-range,
2.A-input and B-input lever switches in AC position,
3.A- and B-amplification controls fully counter-clockwi, variable controls in `cal' position,
4. A and B beam lectors `in'.
5.Time ba control fully counter-clockwi, in `via Y A' position,
6.X-position and Y B-position midrange.
Now switch on the scope and allow 15 c. for warm up.
踔厉笃行7.Apply the signal to be studied to the B-input and the standard signal (from the signal
generator) to the A-input. Note that the A-input signal provides the time ba.
8.Rotate the A- and B-amplification controls clockwi until you obrve a figure of uful
size.
9.Finally, vary the frequency of the standard signal until you obtain a Lissajous figure which淡泊明志宁静致远
is recognizable.
Measuring Frequency
In this experiment the frequency of a signal is measured using the technique of Lissajous figures. The signal who frequency is to be measured is applied to the Y B-input of the scope and the output of a signal generator is applied to the Y A-input (switched to time ba). The two signals thus superimpod at right angles produce a Lissajous figure. Fig. 6 shows two uful ones. Obviously, if
a circle is obtained, the signals are of the same frequency and the value can be read off the dial of the signal generator.
The Experiment
Asmbly and Trial Run母乳喂养好
构成要件
Begin by asmbling the apparatus. Plug the motor which rotates coil S into the variac.
Connect the output of coil S - `Rotating Coil' - to the B-input of the scope and put a Philips
multimeter in parallel with the input. Connect the HP model 200AB signal generator to the A-input
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