Download Microsoft Word - PHY 204 Exp. 1 Electric Field Mapping

Lab 6: Alternating Current I – Magnitudes
Objectives: to Induce an Electric Field which encircles a (negative) Magnetic Field Change –ΔB;
to measure the accumulation of circulating Electric Field into voltage (“EMF” E ) ;
to transform one AC voltage into a different AC voltage in a Power-efficient manner;
to construct circuits with Resistors, Capacitors, Inductors, and diodes and transformers;
to investigate relationship between RMS current and voltage and frequency for devices;
Apparatus:
magnet, pivot, wire coil or solenoid; transformer; resistors, capacitors, inductors
Equipment: Galvanometer (micro-Ammeter), function generator, AC Voltmeters
Background: Force by a magnetic field applied to a moving charge is always perpendicular to the
charge’s motion, so the B-field can never do Work to the charge. This implies that B
cannot change the charge’s Kinetic Energy, so magnetic fields have no scalar Potential
(analogous to gravity’s gh , and electric’s V ). Yet the magnetic field itself does have
1 2
Energy
1 2
E .
field Energy density u B 

B , like the Electric Field’s u E 
8 k
Volume 2
The aggregate B-field Energy in a region (near Qv) must transform
into some other Energy form if the B-field decreases (as Qv slows).
Faraday’s Law: it goes into a temporary Electric field, which
 
 
( B  A)
encircles the negative change in B :  E    
.
t
{the Energy is removed as the induced E does Work on Qv, “to reduce its slowing”.}
This very temporary E-field is said to be “induced” by the change in Magnetic Field –
it is not the static diverging E-field that is “produced” (or exuded or carried) by charge.
Induced Electric field lines form closed loops that curl around the (negative) B-field
change in a right-hand sense (ie, with right thumb along –B , E curls with fingers).
This induced E is most intense at the outer edge of a uniform magnetic field region;
it is spread along a larger circumference (E-line loop), but much more magnetic flux
pierces that larger loop’s Area (perimeter ℓ ~ π d , while Area A ~ π/4 d 2 ).
Induced E-fields are usually fairly weak (if they last long enough to measure easily).
But charge pushed along a circle by E will gain some energy each turn – many turns of
wire coiled along the E-field can accumulate a very high voltage  E·ℓ ! The voltage
from a pickup coil (or transformer secondary) is proportional to its number of turns N .
If some initial B (due to initial source current Is,i ) becomes 0 during time Δt , then
Energy is given to charge flowing thru pick-up coil #2: Q2·V2 = Iavg,2Δt· N2 Δ(B·A)/Δt
. This Energy comes directly from the magnetic field caused by coil #1: B·A ~ N1 I1 r ,
so it comes indirectly from Energy that coil #1’s current put into the magnetic field.
During the original B -field build-up the charges were pushed (by P.S.) against an extra
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potential difference to make the B -field (as well as that due to Resistance “friction”).
So, there’s extra voltage drop in a wire while its current increases, since that increases
the magnetic Energy around the wire. The ratio of voltage over current increase rate is
called (self-)Inductance L = –V/(ΔI/Δt) , which depends on the current’s geometry.
Because wire coils have both resistance and inductance, there are two contributions to
voltage across a wire coil : V = IR + L ΔI/Δt ; only small current can change rapidly.
After any voltage change, the current approaches its new steady value exponentially:
It – I∞ = (Io – I∞) exp(– t R/L) ; inductance in [Ωs] = [Henry] make a unitless exponent.
Activity 1. A. Moving Magnet Near a Wire Coil – Direction
Find out what the galvanometer’s needle deflection indicates about the current thru it:
have the PS push a few microAmp thru a 100[k] resistor in series with galvanometer.
Sketch the Indicated current as arrows into and out of the meter,
and the needle deflection when the current flows that direction.
See if the needle deflects the same amount to the other side, when
the same amount of current flows the other direction through it.
See which way the wire wraps around the solenoid; connect each end
to the galvanometer. Sketch the coil top wire connection ( left / right )
and the coil bottom wire connection to ( left / right ) galvanometer jack.
PREDICT: IF you bring a North magnet pole close to the solenoid coil left end,

show on lower sketch the direction of final B in the coil’s inside Area;
label direction arrows for the change B, and the induction source –B.
With right thumb along –B, right fingers curl in direction of induced E ;
draw this arrow along the solenoid coils, and label it “Eind”.
From which side of the solenoid would this Eind push (+) charges?
Finally, predict the direction of galvanometer needle deflection.
VERIFY: DO move a known North pole to the solenoid coil’s left mouth.
On this diagram, show the actual needle deflection (with magnitude) and
the direction that current flowed thru the coil. This temporary I is called
the induced current … it causes a temporary induced magnetic field …
show the direction of the induced B-field inside the coil.
How is the induced B direction related to the B direction?
Repeat the exercise (new drawing!) for removing the N pole from the coil;
draw & label Bi , Bf , B , –B ; Einduced , I , and needle deflection.
Test your predictions; how is the induced B related to B ?
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Repeat for a South pole approaching the left end of the wire coil;
draw & label Bi , Bf , B , –B ; Einduced , I , needle deflection.
Test your predictions; how is the induced B related to B ?
Repeat for flipping the S pole to the N pole;
draw & label Bi , Bf , B , –B ; Einduced , I , needle deflection.
Test your predictions; how is the induced B related to B ?
Activity 1. B. Moving Magnet Near a Wire Coil – Change Rate
How does the time taken to switch magnet poles influence the induced current?
try 1 second ...
then ½ second ...
then ¼ second ...
needle deflects:
Does the induced voltage increase as the time decreases (proportionally)?
Activity 1. C. Moving Magnet Near a Wire Coil – Relative Motion
Is the same current induced if the coil moves toward the magnet pole?
As the coil face moves toward a N magnet pole, (+) charges in the wire
move thru the B-field’s radial (outward/inward) component. What
direction would the Lorentz Force be on these charges? For coil top,
bottom, front, back : draw qv and B , and deduced F and I .
Activity 2. Voltage Transformer – AC – RMS
Connect a function generator (sine wave) to the transformer “primary”, and connect the
transformer secondary to a 50 Resistor (“load”). Set the hand DMM to measure AC.
At two frequencies, measure the AC (rms) voltage across the transformer’s primary
coil and across its secondary coil. Then switch roles of “ primary” and “secondary”.
f [cycle/s]
Vin [V]
Vout [V]
Vout / Vin
Iout [A]
Does the (Vout /Vin ) ratio increase with frequency (proportionally)?
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Pout [W]
Activity 3. A. Reactance (AC RMS ratio V/I ) of a Resistor
Connect the function generator, thru the (lower) bench DMM set to measure AC mA ,
to the 50[] Resistor. Use the (upper) bench DMM to measure AC voltage. At a
frequency near 300[Hz] , record the AC (RMS) voltage across the resistor and the AC
(RMS) current thru it. Adjust the generator output to a very different voltage, and repeat.
The RMS voltage over RMS current is called “Reactance” (symbol “X”). Calculate the
Reactance for this Resistor at this frequency. What are the units of Reactance?
Then repeat, at a frequency near 3000[Hz] , for two very different voltages.
f [Hz]
Vrms [V]
Irms[mA]
XR=Vrms /Irms [
]
Does the Reactance of a Resistor seem to vary much with voltage? … with frequency?
Is your Resistor’s Reactance close to its “nominal value”?
Activity 3. B. Reactance of a Capacitor
Replace the Resistor by a Capacitor: C = _____ ___ Do trials at similar f and V .
f [Hz]
Vrms [V]
Irms[mA]
XC=Vrms /Irms [
]
Does the Reactance of the Capacitor seem to vary with voltage? … with frequency?
(by the same factor?)
We need to find out how a Capacitor’s Reactance depends on its Capacitance value.
Replace that Capacitor by another, with very different Capacitance: C = _____ ___
Use one of the previous frequencies to obtain the reactance of this Capacitor.
f [Hz]
Vrms [V]
Irms[mA]
XC=Vrms /Irms [
]
How does a Capacitor’s Reactance vary with its Capacitance? (by the same factor?)
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You should have seen small Reactance with high frequency and large capacitance.
Piecing together an experimental “formula” for XC ,
is frequency on top (numerator), or on the bottom? XC = k -------------is Capacitance on top, or on bottom (denominator)?
what are the units of the proportionality constant “k” ?
Use one of your trials to obtain a value for “k” ________ and “1/k” ________
Activity 3. C. Reactance of an Inductor
Replace the Capacitor by an Inductor: L = _____ ___ Do trials at similar f and V.
f [Hz]
Vrms [V]
Irms[mA]
XL =Vrms /Irms [
]
Does the Reactance of the Inductor seem to vary with voltage? … with frequency?
(by the same factor?)
We need to find out how an Inductor Reactance depends on its Inductance value.
Put a piece of iron in the core of the Inductor, which should increase its inductance.
Use one of the previous frequencies to obtain the reactance of this Inductor.
Then replace that Inductor by another, with very different Inductance: L = _____ ___
f [Hz]
Vrms [V]
Irms[mA]
XC=Vrms /Irms [
]
How does the Reactance of an Inductor vary with its Inductance? (by the same factor?)
You should have seen large Reactance with high frequency and large Inductance.
Piecing together an experimental “formula” for XL ,
is frequency on top (numerator), or on the bottom? XL = k -------------is Inductance on top, or on bottom (denominator)?
Use one of your trials to obtain a value for “k” ________ and “1/k” ________
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Lab 6 Summary Sheet
Name :_______________________
Lab Partner : _____________
1. Are all of your results consistent with Lenz’ Law (the induced current produces a
magnetic field that opposes the change in the external field)?
1B. Were your maximum induced currents larger when their durations were shorter?
If they are inversely proportional to each other, what quantity is the same for all?
2. The theoretical transformer voltage ratio is (N2/N1) . Average these for your transformer,
in step-down orientation:
in step-up orientation:
Compare your step-up turns ratio to the reciprocal of the step-down turns ratio:
3. The textbook formulas for Reactances are : XR = R … XC = 1/C … XL = L .
How far off were your “k” values , from 1/2 , and from 2 ? (% error)
What do you think were the main sources of error in this part of the experiment?
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