Download H. Bradt, 37-581, M.I.T. CURRENTS BATTERIES RC CIRCUITS

H. Bradt, 37-581, M.I.T.
CURRENTS
BATTERIES
RC CIRCUITS
CATHODE-RAY TUBE
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H. Bradt, 37-581, M.I.T.
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H. Bradt, 37-581, M.I.T.
X31. Ions in Air; Candle and Electroscope - 5M
Purpose: Demonstrate the existence of ions in air by discharging electroscope with a candle.
Equipment: Candle, shadow-projected electroscope (leaf or Braun?) , electroferous (+ scooper?)
Procedure:
Charge electroscope ES with electroferous EF
Caution: do not blitz leaf ES; use Braun or else transfer charge with a scooper.
Hold candle and bring it slowly up toward ES; watch ES begin to discharge
Move candle away; see discharging stop.
Repeat: move in and then out: get some more discharge.
Move candle in close and see rapid discharge and total discharge
Ref: wl video V27, tape 2, 02:30:27
X31
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Ions
Charged Electroscope
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H. Bradt, 37-581, M.I.T.
X32. Ionic Conduction in Water - 5M --- DANGER: EXPOSED 120 V AC.
Purpose: Show that ions in salt water carry current by lighting 120 V bulb
Equipment: Aquarium with distilled water; salt; H20, light bulb (100 W?, 110V AC), copper-plate
terminals with insulated tabs (handles) to permit motion.
Procedure:
Distilled water in series with bulb and supply
Copper plates hang in aquarium separated by ~25(?) cm
Bulb lights as salt added to water
Drop only ~1/4 tablespoon salt into water between plates
Wait ~30s without stirring (adds suspense)
Bulb then lights up
Move plates closer together, light gets brighter
[I recall that light initially dimmed and then brightened (Probably the first motion
mixed in less salty water?)]
[After each time this demonstration is done, aquarium must be washed very well to remove
salt water. Maybe plates should be sponged too.
Ref: wl video V28; tape 2, 2:32:16
120V bulb
X32
110 V AC
Aquarium
Water
Copper plates (2)
Salt
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H. Bradt, 37-581, M.I.T.
X33. Ohm's Law: A Resistor and a Light Bulb - 5M
Purpose: Demonstrate the relation between voltage and current for a resistor (linear) and for a light
bulb (non-linear and temperature dependent).
Equipment: #49 Light bulb; oscilloscope (projected of course); small circuit box which provides
chopped sawtooth and current-indicating voltage. (Input to the box is sawtooth from oscilloscope.)
Procedure:
Set up:
Truncated sawtooth is the emf that drives the bulb or the resistor.
Linear rise is the relevant circuit input.
Displays are synchronized to circuit input because scope generates original sawtooth
(a) Display EMF vs time t on scope; see saturated sawtooth
(b) Display current i vs t for #49 bulb above variation of EMF.
i is obtained from small R in circuit box
See current rise, peak, and reduce to steady value (peak is due to bulb being cold)
Use 'Single Sweep' on scope: wait ~2 sec and then single sweep
Current peaks much more because bulb is very cold.
Demonstrates change of resistivity (or resistance) as temp changes
(c) Repeat above for 51 ohm resistor in place of bulb
Much less temp. dependence; current tracks form of emf very well (not shown)
(d) Display EMF vs i for 51 ohm resistor
Slope is R: EMF = iR
Use single sweep: still no noticeable effect.
(e) Ditto for bulb
Very non linear - R increases fm ~5 to ~60 ohms
Single Sweep: non linearity even more pronounced
[The cold to hot effect is quite evident, good demo.]
Ref: wl video V26, tape 2, 2:27
SEE FIGURE NEXT PAGE
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B33
em f
(a)
H. Bradt, 37-581, M.I.T.
t (e xpanded)
V i
(b)
51 
R (sma ll)
cold - 1st swe ep
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bulb
warm
em f
t
(trunca te d
sawtooth)
(c)
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resistor
em f
t (e xpanded)
t
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cold
(e)
e mf
resistor
em f
bulb
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H. Bradt, 37-581, M.I.T.
X34. Kelvin Water Drop Generator -5W (1987: postponed to lecture 6W)
Purpose: Demonstrate an interesting application of statics and breakdown.
Equipment: Kelvin Water-Drop Generator (KWDG) apparatus (see sketch); TV projection; lamps
to reflect light off droplets; transparency to explain principle; electroscope. [Used pre-assembled
smaller version of KWDG instead of larger one in video. Larger one harder to set up, but may be
worth it.]
Procedure:
Explain principle with transparency (see sketch)
Hook up to one of the lower buckets and shadow project it.
Start water; watch electroscope charge up (May be slow as starting from zero charge).
Requires some initial assymetry of charge, which is always present
Thus first charging may be slow; starts from 'zero' charge
Later charging faster; residual charge present.
Watch and hear spark breakdown across gap (bottom of figure).
Use neck microphone to amplify sound (shield it from spray).
Electroscope discharges
Watch repeated cycles of charging and breakdown
Water becomes a spray before breakdown (drops repel each other)
After spark, water becomes a stream; sound changes markedly (amplify)
Works quite well; some question about visibility; TV projection helps
Can water drops be seen in TV?
Ref: wl video V33; tape 2, 2:43:10; also V40, tape 3, 3:04:23 (elaborates on the phenomena)
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H. Bradt, 37-581, M.I.T.
B34 Kelvin Water Drop
Ge nerator
E Field
Lines
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Charge d drops
of water
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Ele ctroscope
(Braun?)
SPARK!
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H. Bradt, 37-581, M.I.T.
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H. Bradt, 37-581, M.I.T.
X35. Basic RC Circuit - Very Large Visible Components - 5W
Purpose: Demonstrate the basic RC circuit with highly visible components (a new demonstration).
Use classic galvanometers (projected) to retain transparency of entire circuit.
Equipment: 1k  resistor inside cardboard paper-towel roll which is painted just like a huge
carbon resistor (brown with color-code stripes); large 10 µF can electrolytic capacitor; 2 projected
analog meters (1 zero centered); Large SPDT knife switch.
Procedure:
Zero centered analog (moving needle) meter on overhead projector meter to measure current i.
Analog meter (also projected w. overhead proj.) to measure voltage V across cap.
Close and open switch; watch V and i and explain.
Note slow buildup and saturation of voltage and sharp current spikes
Current reverses when switch opened.
Ref: figure for X36
Time constant  = RC = 10 s; compare roughly to observed rise rime.
Ref: Demonstration X 36 (figure).
Projected Ana log Meters
1k 
B35
A
12V
4
10 µF
50V
Amme te r zero c entered
10
V
H. Bradt, 37-581, M.I.T.
X36. RC Circuit; TV-Projected Oscilloscope - 5W
Purpose: Demonstrate wave forms for RC Circuit with an oscilloscope.
Equipment: RC Circuit driven by square wave generator as shown in figure; 2-trace oscilloscope
Procedure:
Display VR and Vc vs time t on 2 traces of scope.
Shows current i and charge q on capacitor during charging and discharging,
Current: ( i = VR/R) and charge (q = CVc)
Measure RC time; compare to calculated value:
emf = 1 Volt, R = 500 ohm, C ~ 1 µF
 = RC = 0.5 x 10-3 s = 0.5 ms
Compare waveforms to Fig. in text H&R p.709 (hb transparency).
Ref: wl video V58; tape 4, 04:33:55, item 9 of 14.
VC
B36
450 
1 µF
50 
V i
gn d
V
t
t
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H. Bradt, 37-581, M.I.T.
X37. RC Filter with Radio - 5W
Purpose: Demonstrate and discuss principle of a low pass RC filter. (Needs work.)
Equipment: Radio; resistor and capacitor in speaker circuit (or RF side??); large speakers.
Procedure:
Vary values of R and C to change RC time constant.
Show filter can remove high audio frequencies.
Speaker output should be sufficient for lecture hall.
(Amplification with mike and room system is hokey.)
[Note circuit drawn as shown here leads to gain changes which can be confusing when
listening for frequency changes.
This demo did not go well for me; the effect was not sufficiently dramatic or audible.
Seems like a good idea though.]
Ref: Demonstration X63 (Radio filtered with LR circuit).
B37
Speaker
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H. Bradt, 37-581, M.I.T.
MAGNETIC FIELDS
AMPERE'S LAW
BIOT-SAVART LAW
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H. Bradt, 37-581, M.I.T.
X38. Compass Needle and Magnet - 5F
Purpose: Introduce phenomenon of magnetism with compass needle and magnet.
Equipment: Hand magnet and large compass needle, each painted with 2 colors (e.g. half and half so
that one end is red and the other end white) so students can distinguish 2 ends.
Procedure:
Show needle deflected by magnet
Show existence of poles:
Turn magnet around
Opposite end of needle attracted to magnet
Compass needle
X38
N
N
S
S
Permanent magnet
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H. Bradt, 37-581, M.I.T.
X39. Magnet, Nail on String, and Paper Clips - 5F
Purpose: Show magnetic attraction of seeming 'non-magnets' to a permanet magnet.
Equipment: 1/2 of a strong permanent "Magnetron" magnet on a stand; a complete magnetron
magnet with 2 facing poles; nail on a string; box of paper clips; knife blade or equiv.; large compass
needle.
Procedure:
Shadow project both magnets on far wall with arc lamp.
Hang nail upwards, suspended by magnet as shown.
Try different heights;
Put paper between nail and magnet; also knife blade or equivalent to make fall down
Hang a bunch of paper clips on 1/2 magnet
Clips carry magnetism; one hangs from the other; not all touch magnet
Throw handful of clips at 2-pole magnet which seems to reach out and grab them.
[Shadow projection of all this is quite impressive.]
X39
Magnet
Insert paper
or knife blade
Nail
(a)
Lab stand
String
(b)
Paper clips
Magnetron
Magnet
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H. Bradt, 37-581, M.I.T.
X40. Magnetic Field Lines of Bar Magnet - 5F
Purpose: Show form of field lines of a bar magnet.
Equipment: Bar magnet; magnetite (magnetic iron filings?) on overhead projector; blank transparent
sheets of plastic.
Procedure:
Place magnet on projector between 2 sheets of plastic
Sprinkle magnetite filings onto top plastic all around region of magnet
Pattern of filings shows B field lines.
Note similarity to lines one would obtain for E field from 2 charges (stretched out dipole)
Comment on lack of monopoles. (We will show this later.)
Ref: Experiment X67 (Search for Monopoles)
X40
N
S
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H. Bradt, 37-581, M.I.T.
X41. Magnets in Accelerators - 5F
Purpose: Demonstrate use of magnets in high-energy accelerators
Slides: Four 35-mm slides of Cern and Battavia (Fermilab) accelerators. These are located in Bldg. 4
demonstration lab. Also slides of early cyclotrons, etc.
Procedures:
Develop physics of cyclotron (see hb transparency)
Show slides.
Discuss advance from cyclotron to ring accelerators.
Discuss energies attained, diameters, future plans, etc.
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H. Bradt, 37-581, M.I.T.
X42. Force on Current-carrying Wire in Magnetic Field -6M
CAUTION: 12V CAR BATTERY QUASI-SHORTED
Purpose: Illustrate i dl x B force by suspending ('levitating') a wire between 2 poles of a permanent
magnet.
Equipment: Magnetron magnet; heater-cord conductor, adjustable carbon-compression resistor, 12
V car battery; calibrated ammeter, switch, small spring scale
Procedure:
CAUTION: DRAWS LARGE CURRENT; CLOSE SWITCH ONLY FOR A
FEW SECONDS.
Adjust resistor to high resistance by reducing compression.
Close switch momentarily to note current and to note if wire levitates (it doesn't)
(a) Levitate wire.
Reduce resistance several times, closing switch briefly each time, until wire levitates.
i L B force balances gravity:
One needs about 4.4 A at 2.7 ohm to levitate
Use scale to measure force of gravity by lifting wire to
same height it goes when current turned on;
Reading is rough at best, get about 5 gm.
Magnet labeled at 2.2 kG (gauss meter agrees I think)
Pole piece diameter: L = 4 cm
FB = ILB = 4.4 A x 0.04 m x 0.22 T = 0.039 N
Fg = mg = 0.005 x 9.8 = 0.040 N; agrees (too well)
(b) Propel wire upwards.
Reduce resistance to very low value (?? ohms)
Close switch briefly; wire is thrown up well beyond poles by ILB force.
Should measure current. and compare to levitation case.
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H. Bradt, 37-581, M.I.T.
Ma gnet pole
(end on)
X42
Current
ON
OFF
Hea ter wire
Lab stand
A
12V
Car batte ry
Carbon
'compressionadjusta ble'
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H. Bradt, 37-581, M.I.T.
X43. Principle of Galvanometer - 6M
Purpose: Demonstrate principle of galvanometer by hanging coil inside Helmholtz coils.
Equipment: Large Helmholtz coils HC (r ~ 300 mm) ; smaller coil C (r ~ 80 mm) hanging from 2
strings inside HC; large visible wooden arrow taped to inner coil; adjustable DC power supply for
inner coil; scale shown in lower sketch may be omitted.
Procedure:
HC is used as a 'black box' that produces 'uniform' field; will be described more later (in X49)
Explain principle of galvanometer with transparency from text (see hb transparency).
HC has 125 DC applied to it; fixed 10 ohms in series (as usual).
String suspension provides restoring torque for coil C
Adjust current in C and watch it rotate to a new position.
Coil C rotates to try line up mag. moment with HC field
Magnetic Torque balances restoring force of string suspension
Arrow deflects proportionally with current
Position of arrow taped on coil C indicates current in C, a 'galvanometer'
Ref: Experiment X49: Discussion of Helmholtz Coil and measurements of magnetic field.
SEE FIGURE NEXT PAGE
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H. Bradt, 37-581, M.I.T.
Adjustable
Power
Supply
X43
B
Arrow ta ped to Coil C
Side view
(sort of)
Coil C
Strings supporting it
provide restoring
torque
B
Helmholtz Coils
0
+3
-3
Sc ale
B
Top view
Helmholtz
Coil
Woode n Arrow
Coil C
B
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H. Bradt, 37-581, M.I.T.
X44. Deflection of Electrons by Magnetic Field in CRT - 6M
Purpose: Show q v x B force with permanent magnet and electron beam.
Equipment: Cathode Ray Tube and permanent magnet; beam is visible on fluorescent screen inside
tube.
Procedure:
Deflect beam with bar magnet
Hold magnet parallel to normal to fluorescent screen and move it along the normal.
Discuss direction of B field at end of bar and the expected direction of deflection
Use: F = q v x B and F = i dl x B
Could compare to direction of force on a current carrying wire and deduce that charge carriers
in
wire must be negatively charged (where sign of 'positive' current is from convention).
Compare to J.J. Thomson measurement of e/m for the electron with crossed E and B fields.
Fluore scent
scre en
Ele ctron bea m
X44
B
N
Bar magnet
(move along normal
to screen)
S
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H. Bradt, 37-581, M.I.T.
X45. Compass Needle Detecting Magnetic Field from Current in a Wire.- 6W
Purpose: Show that a current gives rise to a magnetic field and its direction.
Equipment: Heater-cord wire carrying large DC current (~10 amps?); on-off switch; compass
needle under wire.
Procedure:
Orient wire north/south more or less
Compass needle orients to magnetic north when current off.
Turn on switch; needle swings from north to east or west.
Shows that there is a magnetic field perpendicular to wire.
In principle, could map out field everywhere around wire and find circular B field lines
X45
Wire (no c urrent)
Compa ss
Nee dle
(points north)
N
Wire with c urrent
B
i
Compa ss
Nee dle
points west
N
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H. Bradt, 37-581, M.I.T.
X46. Magnetic Field Around a Straight Wire; Magnetite - 6W
CAUTION: LEAVE HIGH CURRENT ON ONLY FOR 1 OR 2 SECONDS.
Purpose: Show that magnetic field lines around a straight current-carrying wire are circular and drop
off with distance from the wire.
Equipment: Framed glass plate with straight wire perpendicular to it passing through a small hole;
overhead projector; magnetite (iron filings); variac and transformer to give large alternating current,
~ 50 Amp.
Procedure:
Place framed glass plate on overhead promjector.
Sprinkle iron filings around wire.
Turn on 50-Amp current briefly and tap glass;
See filings form circular patterns with strongest effect near wire.
This demonstration sets up first statement of Ampere's Law
Could measure field everywhere (based on straight-wire case).
Would find circular and falling off as B= µo i/2_r, or 2_r B = µo i.
Integral form of this is Ampere's Law (which is true generally).
[Note: This was done with AC current! I am told that filings will not line up (as well?) with DC
current. Maybe grains just cluster about poles(?) with DC; I did not try it. It is usually presentedto
students as if it were DC; physics of alignment of filings should be interesting. We had a similar issue
with electric fields in expt. X7 ('Dipole Field and Sisal Fibers')]
Ref: wl video V35, tape 2; 02:50:35
Experiments X48 and X50 (same type of apparatus)
X46
Magnetite on
Glass Plate
i ~ 50 Am p (AC!)
Transform er
Leave current on
for only 1 or 2 seconds
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Variac
H. Bradt, 37-581, M.I.T.
X47. Poster of Ampere's Law -6W
Purpose: Congratulate Class on knowing another Maxwell Equation (or 2/3 of one).
Equipment: Cardboard poster - Ampere's Law - suspend over a high rod so I can hoist it up.
Procedure:
Hoist sign up.
This is 2/3 of a Maxwell Eqn. (displacement term is missing.)
Congratulate Class on knowing 1.667 of the 4 Maxwell Equations.
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H. Bradt, 37-581, M.I.T.
X48. Magnetic Field Due to a 'Single Loop' of Current - 6F
Purpose: Show form of magnetic field lines between 2 straight wires which is equivalent to the
inside of a single-turn coil.
Equipment: Framed glass plate with 2 straight wires passing through it and wired such that current is
up in one wire and down in the other; overhead projector; variac and transformer, (and rectifier??) to
obtain 50 Amp.; magnetite filings.
Procedure:
Set plate on overhead projector and proceed as in Experiment X46
Sprinkle filings around wires, turn on variac, tap plate, turn off variac (same as in X46).
Currents up and down in 2 wires is like single loop of coil (dipole) seen from side
Fields coadd between wires; can see it in magnetite
Discuss coil of many turns, fields from each turn add in center of coil like this demo.
[ Requires 50 Amp and tapping to be effective.]
[Note: This was done with AC current but is taught as if DC! See notes in X46]
Ref: wl video V36; tape 2, 2:52:23
Experiment X46 and X50 which use same type of setup.
B48
X48b
B B
Magnetite on
Glass Plate
i ~ 50 Am p (AC!)
Transform er
Leave current on
for only 1 or 2 seconds
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Variac
H. Bradt, 37-581, M.I.T.
X49. Helmholtz Coil - 6F
Purpose: Explain Helmholtz coil qualitatively and to show uniformity of field inside it as compared
to one coil or to regions very near the wires of the coil.
Equipment: Large Helmholtz Coil HC; Gauss meter with probe and projected scale.
Procedure:
Turn on Helmholtz coil; poke probe around to demonstrate uniformity
Turn one coil off; show uniformity is poor
Show field near wire of a coil is stronger
Be sure to use Gauss meter properly, oriented in correct dir. to measure longitudinal field
Probes (or their tips) are designed to measure specific component of field relative to
handle of probe (e.g. parallel or perpendicular).
X49
B
i
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H. Bradt, 37-581, M.I.T.
X50. Magnetic Field from an 8-turn Solenoid; Magnetite - 6F
Purpose: Show form of magnetic field lines in 8-turn solenoid with magnetite filings.
Equipment: Framed glass plate with 8-turn solenoid (length/diameter ~3); overhead projector; variac
and transformer, (and rectifier??) to obtain 50 Amp.; magnetite filings.
Procedure:
Set plate on overhead projector and proceed as in Experiment X46 and X50
Sprinkle filings around solenoid wires, turn on variac, tap plate, turn off variac.
Fields from portions of a single loop coadd
Fields of the several turns coadd; can see it in magnetite.
Note excellent alignment of iron grains; quite dramatic
Discuss coil of many turns, fields from each turn add in center of coil like this demo.
[Requires 50 Amp and tapping to be effective.]
[Note: This was done with AC current but is taught as if DC! See notes in X46]
Ref: wl video V38, tape 3, 3:00:43
Experiment X46 and X48 which use same type of setup.
X50
Ma gnetite
on glass plate
i ~ 50 Am p (AC!)
Transform er
Leave c urrent on
for only 1 or 2 sec onds
28
Variac
H. Bradt, 37-581, M.I.T.
X51. Magnetic Field of a Long Solenoid - 6F
Purpose: Demonstrate magnetic field of a long solenoid; measure field to show matches theoretical
value obtained with Ampere's Law.
Equipment: Long (0.6 m) red solenoid (r ~ 50? mm); ammeter projected; Gauss meter projected.
Procedure:
Measure B in long red solenoid with Gauss meter output (projected full scale is 300 G)
Get ~240 Gauss at 5 A current;
Agrees with calculation:
7 layers @ 300 turns = 2100 turns in 0.6 m
n = 2100/0.6 = 3500 turns/m
B = µoni = 220 x 10-4 T (220 G)
Ref: wl video V39, tape 3, 3:01:42
X51
B
i
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H. Bradt, 37-581, M.I.T.
X52. Biot-Savart Law for Circular Coil - 6F
Purpose: Illustrate use of Biot Savart Law by measuring field at center of a circular coil.
Equipment: Large single coil (can use Helmholtz coil with current in only one coil); Gauss meter
projected.
Procedure:
Turn on coil and measure field at center.
Compare measured value to theoretical value obtained from Biot-Savart Law.
N = 195 (?), r = 0.62/2 = 0.31 m , i = 5A,
B = µ0N i/2r = 19.8 x 10-4 T
Measure ~20 G; agrees with calculation
[NOTE: Coils in the above 2 experiments (#51 and #52) \were connected to same double-throw
switch
for power; the same projected (overhead proj.) ammeter could thus be used for both.]
X52
i
B
Probe
Helmholtz coil
Meter
Magnetic Field
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H. Bradt, 37-581, M.I.T.
MAGNETIC INDUCTION
FARADAY'S LAW
LENZ'S LAW
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H. Bradt, 37-581, M.I.T.
X53. Induction in Fixed Coil with Moving Permanent Magnet - 7F
Purpose: Demonstrate that a moving magnet will induce a current in a nearby coil. No other emf is
required.
Equipment: Coil on (white) stand with projected galvanometer in series; bar magnet.
Procedure:
Stress that there is no external power source
Lift galvanometer out of projector and have student examine it.
Connections to coil are visible and simple
Pass magnet through coil - uniformly all way through
See EMF deflections: 0 , pos , 0 , neg , 0
Move magnet faster, slower, etc. to illustrate rate of change of flux.
Emphasize the magical nature of this phenomenon
Discuss observed phenomenon in terms of changing fluxes through coil
Ref: wl video V41; tape 3, 03:13:02
Coil
X53
Bar magnet
S
N
v
Galvanome ter
G
S
N
v
G
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H. Bradt, 37-581, M.I.T.
X54. Induction in Single-Loop Moving Coil with Fixed Magnetron Magnet - 7F
Purpose: Demonstrate emf developed by moving single-loop coil in presence of magnetic field. This
contrasts with X53 where magnet was moving.
Equipment: Hand-held coil (single loop) of copper wire; projected Keithley meter in series;
permanent magnetron magnet with flat pole pieces.
Procedure:
Position loop so it surrounds poles of magnet (maximum flux threads loop).
Move loop upward past and above poles (until no flux threads loop; see sketch next page)
Changing flux gives rise to emf and current .
Note current on meter
Keithley meter set on AMP: Full scale i = 10-4 x 0.003 = 3 x 10-7 amp
Keithley Multiplier of 10-4 means internal R = 104 ohm;
Measure approx. full scale: thus EMF = iR = 0.003 V
Agrees with calculation if one uses 0.1s for time flux was changing (seems too short)
 ~ 0.2 T x (0.04 m )2 = 3.2 x 10-4 T-m2
EMF = - /t = 3.2 x 10-3 V = 3.2 mV
1987: Set meter at center zero and 0.01 x 10-4 scales.
Full 1/2 scale measured which is 1/2 x 0.01 V or 0.005 V or 5 mV (about OK)
See next page for diagram and logic of this demo.
NOTE TRANSMITTER MIKE GETS INTO KEITHLEY; TURN IT OFF & SHOUT!
SEE FIGURE NEXT PAGE
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H. Bradt, 37-581, M.I.T.
B54
Ammeter
d  B
dt
=
i> 0
v
Coil moving up
d B
dt
B
< 0
i
S
i
> 0
Note: The vector S is a
surface vector, not a
south pole.
B
i
B
F
B
M A GN ET
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H. Bradt, 37-581, M.I.T.
Procedure to find current from Faraday's Law (Ref. Sketch above)
1. Create a positive S (surface) direction for flux B.
2. Deduce (RH coord sys.) positive direction around loop
for emf and current.
3. Deduce flux change dB/dt for the given problem.
4. Use Faraday's Law to deduce emf direction (and mag.)
5. Use Ohm's Law to get current i; same dir as emf.
Find force F and "induced" field Bi in loop due to induced current i (See Fig.)
6. F = i dl x B is down. (opposes motion - good thing!)
7. Flux of B in loop due to induced current is to right (fm RHR or BS Law)
tries to maintain flux through coil.
Put coil back in magnet:
8. Apply F.L.; get opposite direction for emf, i, and Bi.
9. Note induced Bi is (again) in direction trying to maintain flux at its
initial value of zero.
LENZ'S LAW: Items 6 and 7 above are the bases of the two versions of Lenz's Law.
Note that they are both follow from Faraday's Law.
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H. Bradt, 37-581, M.I.T.
X55. Faraday's Law; Wire Loop Around a Solenoid - 7F
Purpose: Show that changing flux threading a one-turn coil produces an emf even though there is no
motion and that a 2-turn coil yields twice the emf.
Equipment: Solenoid (large red); power supply and switch for solenoid; flexible single-wire loop of
Cu wire plugged into Keithley meter with BNC connector (same coil as in X54); Keithley meter is on
zero-centered scale (see X45 description) and projected.
Procedure:
(a) Single loop around solenoid
Loop the coil around the solenoid (see sketch)
Loop goes around entire coil and stand.
Prop up coil on blocks so end of stand is clear of, and above, table.
Turn solenoid on and off
Watch emf (curent) jump negative and positive; note maximum amplitude.
(b) Change shape of loop (bunch it up)
Coil remains looped once around solenoid
Note that the amplitude of the excursions of the emf remain the same as before.
(c) Reverse loop; jumps of emf do not change shape (I did not do this step)
(d) Double up loop to 2 turns; it barely fits over solenoid and its stand.
Twice the emf is seen.
Ref: wl video V43; tape 3; 03:17:03
NOTE: MIKE TRANSMITTER CAN SCREW UP KEITHLEY; TURN IT OFF
X55
Solenoid
Power
supply
Meter
36
H. Bradt, 37-581, M.I.T.
X56. The Generator; Large Coil Rotating in Earth's Magnetic Field - 8M
Purpose: Illustrate the principle of the generator by rotating a coil in the earth's magnetic field.
Equipment: Large coil (D = 0.5 m; yellow and red) with slip rings; Keithley (?) meter projected.
Procedure:
Slip Rings carry current.
Rotate coil by hand about 1 revol. per second.
Output goes to electrometer or multimeter - projected
Note (approx) sinusoidal output: EMF proportional to current
Note phase of output; max emf when loop approx. vertical
As expected for an approx. vertical field; (t is maximum)
This is a "Generator"
Mag Field in Boston (1965); should check later date
B ~ 0.56 G; Dip angle 73o nearly vertical
N = 42 turns, D = 0.515 m; A = 0.21 m2
emf = - N t = 42 x 0.56 x 10-4 x 0.21/ 1.0 sec. = 0.5 mV
Omitted this calculation last 2 years; Experiment X54 had similar calculation
Ref: wl video V45, tape 3, 03:20:30 (may be different apparatus but I doubt it)
X56
Rotation
axis
Coil
B
~70
o
Magnetic
north
Slip rings
Meter
37
H. Bradt, 37-581, M.I.T.
X57. Lenz's Law; Copper Pendulum in Magnetic Field - 8M
Purpose: Demonstrate braking via eddy currents in pendulum; eddy currents arise from magnetic
induction.
Equipment: Pendulum with flat copper plate for 'bob'. Electromagnet with poles through which
pendulum swings; a duplicate flat plate 'bob' but with slots in it; TV projection of apparatus.
Procedure:
Magnet off: demonstrate that pendulum swings freely.
Magnet on: release pendulum from large excursion
Pendulum brakes dramatically when it enters field of magnet.
Induced currents - eddy currents - damp oscillations
Substitute slotted pendulum:
Braking is much reduced; slots inhibit induced currents.
Direction of eddy current loop can be deduced from emf = -/dt (see sketch)
Using this current, F = i dl x B gives force opposing motion.
i dl
B57
F
Pendulum
v

B
em f   i
B (into pape r)





 


 


 






38
Slotte d
pe ndulum
H. Bradt, 37-581, M.I.T.
X58. Induction; the Shooting Ring with DC Power - 8M
Purpose: Illustrate Faraday's Law by propelling conducting ring upward by increasing magnetic flux
through it.
Equipment:: Electromagnet with iron-wire core projecting above it; conducting ring that fits around
core, switch, 120 VDC supply; resistor (10 ohms; heater coils) in series with electromagnet; project
ring with TV system (close up view because ring only jumps a few inches).
Procedure:
Setup:
Use 120 V DC (DIRECT CURRENT)
The 10 resistor matches the 60-Hz impedance when done with AC)
Stress that ring not connected to anything
Sketch field lines, flux change, current, and F = i dl x B(see sketch below)
Applies to time just after switch closed
Field lines flare out so that net force is up
Close switch; ring jumps up about 10 cm.(only)
Repeat with slotted ring; does not jump
Repeat with both rings: slotted ring below, then above - for fun.
[Very effective if billed as spectacular that ring jumps (all by itself!); good TV helps
This experiment usually done with AC but explained as if it were DC!
With AC Power, the ring flies up to the ceiling.
We will use AC later to illustrate phase shifts in LR Circuit.
Refs: Expt: X78 where done with AC; cf. wl video V44, tape 3, 03:19:25
39
H. Bradt, 37-581, M.I.T.
X58
B
B Field Line s
(increa sing)
F
Ring
Core of
iron wire s
i
i
Aluminum
Ring
i
Force has upwa rd com pone n
Current
coils
(Current
increasing)
F = i dl x B
This sketch a pplie s to ti
me just after the switch
40
is c lose d.
t
H. Bradt, 37-581, M.I.T.
X59. Poster with Maxwell Eqn. "Faraday's Law" - 8M
Purpose: Stress progress in course
Equipment:: Large cardboard with Faraday's Law written on it.
Procedure:
Hoist sign with string
Now we have 2.667 Maxwell Eqns.
Congratulate class.
41
H. Bradt, 37-581, M.I.T.
LR CIRCUITS
MUTUAL INDUCTION, ETC.
42
H. Bradt, 37-581, M.I.T.
X60. LR Circuit Driven by Square Wave - 8W
Purpose: Illustrate wave forms in an LR circuit driven by a square-wave emf with a projected 2sweep CRT display.
Equipment: LR circuit (see sketch); Inductance is the red solenoid (Rint = 10 ; L = 73 mH);
External variable resistance set at 90 ohms (i.e. Rtotal = 100 ); CRT (2-sweep) displayed with TV.
Procedure:
Drive circuit with square wave (and also single step function?)
Project VR and VL vs time on same CRT; VR is measure of current
Measure time constant t on scope; compare to predicted value
t = L/R = 0.07/100 = 0.7 ms
Change resistor R; watch time constants change on CRT
Change L by putting iron wire bundle in solenoid gradually: L  ~1.0 H
Again note time constant changes.
Note: The quantity VL measured by the scope is the emf generated in the inductor by the changing
flux. Beware of refering to VL as an ordinary potential difference; if one carries a charge around the
circuit, the net work E.dl integrated around the circuit is non-zero!
43
H. Bradt, 37-581, M.I.T.
V
R
R
X60
L
Emf
V ~i
R
V
L
44
V
L
H. Bradt, 37-581, M.I.T.
X61. Time Constant in LR Circuit; 30-Henry Coil and Light Bulbs - 8W
Purpose: Demonstrate LR time constant in a transparent manner by watching the current build up in
a large magnet with a 7s time constant and noting the 7-s delay with a 100W? light bulb. Show large
emf developed when circuit interrupted by dumping current through 120V light bulb.
Equipment: Big 30-Henry coil with 4.5  internal resistance, two 6V Light bulbs (to sense applied
voltage and current), 12 V car battery, external resistor R = 4.5 , switches; 110 V (25W?) bulb.
Bulbs have 0.2 ohm resistance when cold.
Procedure:
Switch A applies voltage to circuit
Switch B permits substitution of resistor for the solenoid (removes inductance)
(a) Load is external resistor; Switch B down
Close Switch A in series with battery
Both 6V lights light "instantaneously"
Demonstrates role of the 6V indicators when inductance in circuit is small.
Open switch A
(b) Repeat with inductor as load; Switch B is "up"
Voltage bulb lights instantaneously (sort of) when switch A closed
Current bulb lights in ~7 seconds
Compare to expected value:  = L/R = 30/4.5 = 6.7.
(c) OPEN Switch B while steady current flowing through inductor
Inductor discharges through 110V (25W?) bulb
Burns out bulb (maybe); flashes very bright at the least..
Illustrates emf that develops in inductor when circuit interrupted
Ref: wl video V51, tape 4, 04:04:50, 2nd of 14.
NOTES: (1) Voltage light C was lighting slowly (~ 1 sec) in 1986, it was better in 1987. I forget what was fixed; the
inductance of the coil resistor in series with bulb C or the bulb itself could have been the problem. One should probably
use a 12V bulb and no series resistor (2) I recall that in 1986, the 110V bulb would blow out; in 1987, we could not get it
to do so. We tried several wattages. Check the diode: at one point it was reversed; note that the experiment will appear to
work OK even if the diode is shorted (because of the relatively high resistance of the 110 V bulb).
45
H. Bradt, 37-581, M.I.T.
Solenoid (30 H, 4.5
) 
B61
B
E
110 V bulb
Measures
current
4.5 
D
6V bulb
C
Measures
voltage
(should try
12 V bulb and
no resistor)
6V bulb
12 V
A
46
H. Bradt, 37-581, M.I.T.
X62. Arcing when Switch on Inductor Opened - 8W
CAUTION! DANGER!
Purpose: Illustrate dramatically the large emf developed when the switch on a large inductor is
opened.
A huge arc is created.
Equipment: Biggie Magnet with rounded pole piece (L ~ 12 H?, R = 1.4 ); R ~ 4.5  series
resistor (permanent large rheostat under bench in 26-100); switch with long plastic handle; 250 (or
120) V, 40 amp DC supply; ammeter (projected?). [Projection of ammeter not done before; seems
like a good idea.]
Procedure:
Use 250 V or 120 V DC supply. 250V was used in 1984-6; 120 V was used in 1987 'for
safety'. The latter gave quite a good spark, not too reduced from that with 250 V.
Close switch and watch current build up to 30 A (120 V) or to 40 A (250V).
Ammeter to see current increase.
Maximum current is adjusted with big "rheostat"? below table
Stand back from switch; 'throw' switch open; see huge spark
Long plastic handle on switch for safety
Calculate energy U stored when current flowing.
If 40 Amp, U = 1/2 L i2 = 1/2 12 (40)2 = 9600 Joules
Explain origin of arc: Inductance acts to keep constant current flowing in circuit when switch
opened. Opening of switch introduces huge resistance in circuit (air); hence huge emf
required to maintain current which appears as an arc.
B62
L = ~12 H?; R = 1.4

~ 4.5 (series R
under lab be
A
250 V DC Power Supply
(120 V in 1987)
47
Amm eter
nch)
H. Bradt, 37-581, M.I.T.
X63. Frequency Response of LR Circuit - Radio Filter - 8F
Purpose: Demonstrate that an LR circuit can act as a low-pass filter in a radio. [Needs work.]
Equipment: Radio with low-pass LR filter (in speaker circuit?); variable resistor and variable
inductance; speakers sufficient to be clearly heard throughout hall.
Procedure:
Play radio (music and voice); vary L and R
High frequencies cannot get through LR circuit.
[This was a bust in 1987; needs work. Volume not loud enough could not hear pitch
distinctions
when L or R changed. Maybe resistor had inductance. Was OK in '86!]
Ref: wl video V52, Tape 4; 04:07:40, 3rd of 14.
L
B63
~
R
48
H. Bradt, 37-581, M.I.T.
X64. Opening and Closing Switch on Large Inductor; Transients on CRT - 8F
Purpose: Demonstrate the emf obtained when the switch in series with an inductor is closed and
opened. Uses setup students have already seen (sketch for X61).
Equipment: Same large 30-H magnet and setup seen in figure for X61; magnet has closely-spaced
flat pole pieces;
Procedure:
Unscrew 120V bulb to take protection diode out of circuit
Put CRT 1/10 probe across magnet
Least sensitive scale and on "AC"; very slow sweep
Sweep bright so can see fast spike.
(1987: used storage scope; maybe different probe.)
Open and shut switch B with small delays (~ 1 sec)
Spike on opening should be bigger
Delay more and more before opening
More current flowing gives bigger and bigger spike when opening
Opening switch is like putting very big R in circuit
EMF generated is enough to keep current going, i.e. huge.
49
H. Bradt, 37-581, M.I.T.
X64 (See Circuit, Fig. X
61)
CRT Face
Close
switch
Open
Close
Open
switch
t
t
Short tim e (~2 second) be
closing and opening switc
tween
h
Longer time (~5 second) b
closing and opening switc
50
etween
h.
H. Bradt, 37-581, M.I.T.
X65. Faraday's and Lenz's Laws; Ring Falling in Magnetic Field - 8F
Purpose: Illustrate Lenz's Law by dropping conducting ring through poles of a strong magnet. Ring
falls slowly when entering and leaving field (flux changing) and fast when totally inside poles (flux
not changing).
Equipment: Big 30-H magnet with closely-spaced flat pole pieces spaced about 5? mm (Same
magnet we used earlier - with 3 light bulbs; see circuit for X61); flat conducting ring of diameter
about 1/2 the vertical extent of pole pieces; similar flat ring which has a gap in it; shadow project the
pole pieces from side with arc lamp and Fresnel lens so shadow is on far wall with gap seen as in
sketches below. Also set up TV camera to show closeup of setup. (See notes below.)
Procedure:
Explain setup using TV projection system.
Adjust lights so shadow projection is effective
(a) Magnetic field OFF
Drop ring through poles with magnetic field off; ring falls straight through
(b) Magnetic field ON.
Explain what to expect when field is ON from Lenz's Law (or Faraday's Law).
Drop ring again
Ring drops slowly as enters, fast in uniform field, slow again as it emerges.
(c) Ring with gap in it.
Repeat (b) with magnetic field ON. Ring falls through fast.
[1987: Used TV to view ring; Shadow projection used previous years was very dramatic but
harder to set up. Students see huge shadow; changing speed of dropping ring very
impressive.TV cannot follow ring between poles as well as shadow. TV does show the setup well.
Probably best if both shadow and TV could be done; must switch lights on and off.]
SEE FIGURE NEXT PAGE
51
Ring
X65
(b)
Pole pie ce
H. Bradt, 37-581, M.I.T.
Drops slowly
(a)
(c)
Ma gnetic
field
Drops fast
(e)
(d)
Slowly
Fre e fa ll!
DONG!
52
H. Bradt, 37-581, M.I.T.
X66. Mutual Inductance; 2 coils - 8F
Purpose: Demonstrate mutual inductance with 2 coils by starting and stopping current in one coil .
Equipment: Two identical coils on stands; dry-cell battery (12V?); switch; galvanometer
Procedure:
Hook up componets as indicated in sketch.
One coil has 12V battery and switch in series with it; the other has galvanometer
Close switch
(a) Motion of one coil changes flux through the other.
Move one coil (#1 or #2) toward/away the other, thus changing flux through #2..
Galvanometer shows emf in #2
(b) Open and close switch in #1circuit
Coils should be relatively near each other.
Note emf jumps in circuit #2.
(c) Move coils closer together (or further away) and open/shut switch as in (b)
Shows more linkage when coils are near one another
[Would expect to obtain emf > 12V when switch opened?
(See no difference. Why? Galvanometer time constant too long? Check with scope.)
Ref: wl video V42, tape 3, 03:14:08
X66
Coil #1
Coil #2
Projected
ga lvanom eter
12V ?
dry cell
G
Stand
Stand
53