241 Solenoids

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Physics 241 Lab: Solenoidshttp://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html

Name:____________________________

Section 1:

1.1. A current carrying ire creates a magnetic !ield around the ire. "his magnetic !ield may be

!ound using the #iot$%a&art 'a d

B= µ o

4π

I ⋅d s×r

r 2

. (oe&er) this la can be di!!icult to use. *!

there is a high degree o! symmetry) you may choose to !ind the magnetic !ield produced by the current

carrying ire using Ampere+s 'a

B • d

s

w h o l eA m p e r i a n

l o o p

= µ o I to ta l en c lo sed b y

A m p e r i a n lo o p . Ampere+s 'a simpli!ies !inding a

magnetic !ield in the same manner that ,auss+s 'a simpli!ies !inding an electric !ield.

-amine the ideal solenoid also called inductor here a &ery long coil o! ire carries a

current * is !ound to ha&e a nearly uni!orm magnetic !ield inside the coils and a nearly zero magnetic!ield outside the coils. A cross sectional picture is pro&ided:

*n the laboratory) an eperimenter may easily control the current through a solenoid) and so it is

desirable to determine the strength o! the magnetic !ield inside the solenoid as a !unction o! the current.

#ecause o! the high degree o! symmetry in the ideal solenoid) Ampere+s 'a may be used to !ind themagnetic !ield inside the solenoid. ,o o&er the !olloing deri&ation ith your lab partner since you

ill need to understand it !or your lab report. Explain each step beside the given derivation:

http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html

http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html

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1.2. 3hen the current in a ire changes) the strength o! the magnetic !ield created by the current

also changes. "here!ore) i! you no the time dependent beha&ior o! the current) you can !ind the timedependent beha&ior o! the magnetic !ield inside the solenoid. *! the solenoid is carrying a sinusoidally

oscillating current) hat ind o! time dependence o! the &arying magnetic !ield inside the coils. Your

answer:

1.5. A solenoid ith 56)000 loops per meter is placed in series ith a 10 Ω

resistor and dri&en by a sinusoidally &arying source &oltage. 7sing an

oscilloscope) the &oltage across the resistor is !ound to be V res(t )=4.2sin325(. 3rite a time dependent e8uation ith numerical &alues to describe the time

dependent strength o! the magnetic !ield inside the solenoid. "hen pro&ide tospeci!ic times hen the current and magnetic !ield ha&e both simultaneously

reached their respecti&e amplitudes. Note that µo94π10$ ;"m/A<.

Your answers:

Section 2:

2.1. "o &ery important concepts in the study o! electricity and magnetism are Ampere+s 'a and

=araday+s 'a. Ampere+s 'a states that a current in a ire creates a magnetic !ield. =araday+s 'astates that i! the magnetic !ield changes oscillates the changing magnetic !ield ill create a &oltage in

the ire. "his &oltage that is created by the changing magnetic !ield is call the bac ->= or thesel!$induced ->=. "hus the logical !lo o! ideas is the changing current inside the solenoid wirecauses a changing magnetic field between the solenoid coils that then causes a changing back EMF

inside the solenoid wire. "his is shon graphically !or a sinusoidally oscillating circuit ith a resistor

and inductor in series:

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2.2. -perimentally obser&e the ?0o phase shi!t that shos that the oscillating &oltage across an

inductor leads the oscillating &oltage across a resistor by π/2. 7se a sinusoidal source &oltage to dri&e

an inductor in series ith a resistor. 7se your oscilloscope to measure the &oltage across the resistor

and inductor simultaneously so that you can &ie the ?0o phase shi!t. >ae a 8uic setch o! your

obser&ations belo. @ecord your choices !or resistance &alues) dri&ing !re8uencies) etc. that enabledyou to see the inductor lead the resistor.

Warning: at very low frequencies, the self-induced back EMF goes to zero because d!dt is

nearly zero so you would think that you would measure zero volts across the inductor" #owever, these

inductors have $% km of wire and therefore some small resistance so at low frequencies you mayregister the voltage dro& of the solenoid acting as a &ure resistor" 'n this case, there is no &hase shift"

(heck for yourself that the solenoid acts as a &ure resistor at very low frequencies $%) #z"

Your parameter choices and uic! s!etch:

2.5. *! a magnetic !ield is changing through the area o! a loop o! ire) then =araday+s la says thatthis changing magnetic !ield ill induce a negati&e &oltage called the bac ->= in the circuit:

• =araday+s la: ε L(t )=−d φ

B

dt )

here the magnetic !lu φ# is simply the magnetic !ield integrated o&er the cross sectional area o! the

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ire loop:

• >agnetic !lu: φ B=

Aarea•

.

%ince a solenoid has N loops each ith a cross sectional area that is constant in time) this means that:

• =araday+s la !or !ied area and N loops:

ε L(t )=− NA

d

dt .

ue to the ay e thin about electronics) e need to remo&e the negati&e sign !rom thise8uation. "his is similar to our use o! B9*@ !or resistors in a circuit hen technically the resistor

causes a &oltage drop there!ore a negati&e &oltage change. Another ay to thin about this is that e

can say that due to conser&ation o! energy) adding all the &oltages in a circuit together should yield

zero: V source−V

resistor = #ut e can alays rearrange to ha&e V

source=V

resistor "hus you should

rite ε L(t )= NAd

dt hen describing the electromoti&e !orce o! a solenoid.

2.4. =ind the time dependent bac ->= created by the @' circuit gi&en in section 1.5. i! the crosssectional area o! the inductor is 0.00C m2 and the inductor is ? cm long. Your answer:

@estating the ideas o! the pre&ious section) i! you tae a single solenoid and apply an

alternating source &oltage) then it ill ha&e an alternating current. "he alternating current o! this

single solenoid ill produce an alternating magnetic !ield ithin the area o! its on coils. No) there

is a changing magnetic !ield ithin the area o! the coils. "he changing magnetic !ield induces a&oltage in this solenoid the bac ->=. "his process is called sel"#inductance.

"he parameter ' %* units o! (enry is used to describe the solenoid+s ability to sel"#induce a

bac ->= ε'. "his parameter is de!ined as:

L solenoid = ε

L(t )

dIL

dt

.

%ubstituting the pre&ious results ε L= NAd

dt and

Binsidesolenoid

= µ onI

L gi&es:

L solenoid

= NA

dB

dt

dIL

dt

= NA dB

dIL

= A⋅ µ

o⋅ N ⋅n.

2.5. =ind the sel!$inductance parameter ' !or the inductor described in sections 1.5. and 2.5. Your

answer:

2.4. *! you allo a magnet to sing at the end o! a pendulum Dust barely abo&e some nonmagnetic

sheet o! copper) the pendulum$magnet ill lose energy and come to a stop. -plain here the energy

goes using the concepts o! eddy currents E'enz+s 'a. Your explanation:

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Section $:

5.1. No you ill eperimentally eamine the magnetic !ield produced by a solenoid ith current

!loing through it. Note that a real solenoid produces a magnetic !ield 8ualitati&ely similar to a bar

magnet o! the same dimensions.=irst chec that your compass has not been !lipped. "he compass arro should align itsel!

ith the local magnetic !ield produced by the -arth. @emember that the -arth+s north magnetic pole is

at the geographic south pole. "his causes the local magnetic !ield to point toard the north geographic pole. "he compass aligns ith this magnetic !ield and thus points toard the north geographic pole. *!

your compass has been !lipped) !i it ith a strong magnet or tell your "A so they can !i it.

-amine the direction o! the indings o! your solenoid. Fou can tell hich ay the current

circulates by ho the ire enters the solenoid. "hen you can use the right$handed scre rule todetermine the direction o! the magnetic !ield inside the solenoid hich side is north and hich is

south.

Apply constant current using the constant &oltage supply a !e &olts should be good to yoursolenoid. 7se the right$handed scre rule to predict the positi&e direction north pole o! the magnetic

!ield produced ithin the solenoid and the magnetic !ield surrounding the solenoid in general. "est

your prediction using the compass and setch the magnetic !ield surrounding the solenoid belo. #esure to dra your solenoid in such a ay as to sho the reader ho the current !los through the

solenoid see pre&ious pictures in this manual !or hints.

Your s!etch o" the observed magnetic "ield within and surrounding a real solenoid with constant

current:

Section 4:

4.1. *n this section you ill eperimentally obser&e the process o! sel!$inductance. Glace a solenoid

in series ith a 100 Ω resistor and dri&e this simple @' circuit ith a sinusoidal source &oltage ith 10

(z &ery slo and 10 to 20 &olts source amplitude. %et your oscilloscope to measure the &oltage

across the resistor. "he resistor &oltage tells you ho much poer the circuit is remo&ing !rom the

!unction generator. "his also tells you about ho much current is !loing through the resistor andthere!ore the solenoid.

Hualitati&ely eamine hat happens to the current in the solenoid &ia resistor &oltage as you

increase the dri&ing !re8uency !rom 100 (z to higher !re8uencies. Your observations:

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"he impedance χ' o! an inductor is !ound to be χ L =ω drive here ' is the sel!$inductance

parameter o! the solenoid and ωdri&e is the angular dri&ing !re8uency. "he total circuit impedance

ithout a capacitor is gi&en by Z = R2+ χ L

2. %ince I resistoramplitude

=V source, amplitude

Z

) eplain ho *@

ould change i! ωdri&e as increased. "his is an alternate eplanation o! the pre&ious 8uestion. Your

explanation:

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Section %:

I.1. @estating pre&ious ideas) =araday+s 'a states that a changing magnetic !ield ill induce a

bac ->= &oltage: ε L =−

d φ B

dt . "echnically this e8uation shos that the bac ->= produced is

proportional to the rate o! change o! the magnetic !lu) but the magnetic !lu is Dust the magnetic !ield

integrated o&er the sur!ace area o! the circuit. *n simple situations this Dust becomes

d φ B

dt =dA⋅ B( )

dt = A

d

dt . %ince the presence o! a bac ->= is e!!ecti&ely lie adding a battery to a

circuit) a current can be induced in a circuit ithout any other &oltage source presentJ

An eample o! this interesting situation is hen a magnet approaches a solenoid in series ith aresistor:

(ere the magnet+s north pole is approaching the solenoid !rom the le!t. "he magnetic !ield

strength is groing inside the inductor coils as the magnet approaches dB

dt >0. 'enz+s 'a is a &ery

simple rule that allos you to !igure out the direction o! the current !lo caused by the induced bac

->=. 'enz+s 'a states that the bac ->= ill cause a current that generates it+s on reactionary

magnetic !ield that opposes that change o! the magnetic !ield inside the solenoid. *n this case themagnetic !ield is groing to the right. "here!ore) 'enz+s 'a states that there ill be a reactionary

magnetic !ield groing to the le!t:

No you can simply use the right$hand scre rule to !ind the direction o! the current tra&eling

around the inductor coils that ill produce the correct reactionary magnetic !ield and trace this current

through the ires to !ind the direction o! the current through the resistor.

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I.2. No sol&e some simple applications o! 'enz+s 'a and the right$hand scre rule !or !inding

the current induced in a circuit ith no source &oltage present.

Your answer:

Your answer:

Your answer:

Your answer:

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Section &:

C.1. No you ill eperimentally obser&e ho a changing magnetic !ield induces a &oltage in anunpoered solenoid. Khec your bar magnet ith your compass to see that it is labeled correctly.

@emember that the compass+s needle labeled north should point to south magnetic poles lie the

north geographic pole o! the earth.(oo up your solenoid to the oscilloscope so you can measure the electric potential di!!erence

beteen both ends. on+t bother placing a resistor in seriesL there on+t be large enough currents to

measure ith the oscilloscope. *nstead you ill Dust eamine the direction o! the bac ->= bychecing the sign o! the &oltage across the solenoid caused by the bac ->=.

C.2. >o&e the north pole slowly toard one side o! your solenoid. 3rite hat you see on your

oscilloscope positi&e or negati&e induced &oltage. Fou should see some induced &oltage or you aremo&ing too sloly. "ry using I00 ms/di& and I0 mB/di& to clearly see the response. Your

observation:

C.5. >o&e the north pole uic!ly toard same side o! your solenoid as in C.2. 3rite hat you seeon your oscilloscope and compare the amplitude o! the induced &oltage ith part C.2. Your

observation and comparison:

C.4. 7se the e8uation !or =araday+s 'a ε L =−

d φ B

dt to eplain hy the amplitude C.5 as larger

than C.2. Your answer:

C.I. No mo&e the south pole uic!ly toard the same side o! your solenoid as in C.2. 3rite hat

you see on your oscilloscope and compare your result ith that o! C.5. Your observation and

comparison:

C.I. 7se 'enz+s 'a to eplain the di!!erence beteen your obser&ations in C.5 and C.I. Your

explanation:

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Section ':

.1. *! you tae a solenoid and dri&e it ith an alternating current) it ill produce an alternatingmagnetic !ield inside its coils. *! you then tae another solenoid that is unpoered and place it nearby

so that the changing magnetic !ield o! the !irst solenoid reaches inside the coils o! the second solenoid)

then a &oltage ill be induced in the second solenoid des&ite the fact that the wires of each solenoid in

no way touch each other . "his is the process o! mutual inductance and is the basis o! transformers in

transmission lines.

"he de!inition o! the mutual#inductance is:

M transmitterto receiver

= ε receiver

− dItransmitter

dt

.

"he mutual inductance parameter > can be used to encapsulate all the geometric in!ormation

o! the combined solenoids. *t is used in engineering so that you can calculate the transmitted &oltage

!rom an applied current ithout ha&ing to calculate the magnetic !ield and geometric !actors."he e8uation !or > is true !or all times so it is easiest to determine it eperimentally using the

time hen the right hand side components ha&e simultaneously reached their maimums:

M transmitter

to receiver

= ε receiver, amplitude

dItransmitter

dt amplitude

%ome digital oscilloscopes can measure deri&ati&es in hich case you could determine the

denominator usingdItransmitter

dt

amplitude

=1

R

dVresistor, transmitter

dt

amplitud

. *! not) you ould ha&e to tae

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the deri&ati&e yoursel! to !ind that

dItransmitter

dt

amplitude

=ω

RVresistor

transmitteramplitude

.

(ot a uestion)

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Section *:

6.1. *n this section you ill eperimentally study the process o! mutual inductance. 7se a !unctiongenerator to dri&e a solenoid ithout any resistance. 7se a sinusoidally oscillating source &oltage o!

10$20 &olts amplitude. "his solenoid is the transmitter .

(oo up the other undri&en solenoid directly to the oscilloscope. "his solenoid is essentiallythe receiver . Glace the solenoids together as close as possible so that you can measure the maimum

induced &oltage amplitude in the recei&er. Glacing so!t iron inside the coils can increase the magnetic

!ield inside the solenoids so that transmission is increased.

6.2. No create a graph shoing the

maimum induced &oltage amplitude in the

recei&er !or se&eral di!!erent dri&ing!re8uencies. Kollect about 10 data points it is

isest to !ind ! ma transmission !irst and collect data

on either side. "hen use your data to create agraph. A poor eample o! hat you should see

is pro&ided. =ind the !re8uency that maimizes

transmission. +ollect your data in the space

below, ma!e your graph on graph paper, andreport your maximum transmission

"reuency below:

6.5. 7se the mutual inductance e8uation and the sel!$inductance e8uation to eplain hich part o!

your graph is dominated by mutual inductance and hich part o! your graph is dominated by self-

inductance. #e sure to chec your anser ith your "A. Your thorough explanation:

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Section -:

?.1. 3hen you measure B@) amplitude 9 ε') amplitude) then you no that that χ' 9 @. *! you !ind the

!re8uency here this happens) you can use χ L =ω drive to !ind '. 7se this single measurement

method to !ind ' !or your solenoid. Your answer:

?.2. "here is a second multi$measurement method to !ind '. "he &oltage amplitudes o! thesinusoidally dri&en @' circuit are &ery similar to those !or the sinusoidally dri&en @K circuit you

encountered a !e ees ago:

V (t )resistor = R

Z V source

amplitude

sinω drivet ( and V (t )inductor = χ L

Z V source

amplitude

sinω drivet +π

2

.

"his gi&es the !olloing relationships !or the amplitudes:

V resistoramplitude

=

R

Z V source

amplitude

and V inductoramplitude

=

χ L

Z V source

amplitude

.

i&iding these to e8uations gi&es

V i n d u c t o ra m p l i t u d e

V r e s i s t o ra m p l i t u d e

=

χ L

⋅ V s o u r c ea m p l i t u d e

Z

R ⋅ V s o u r c e

a m p l i t u d e

Z

= χ

L

R

. "here!ore) χ L= R

V inductoramplitude

V resistoramplitude

.

*n order to test the relationship χ L =ω drive and eperimentally determine ' !or your solenoid) simply

combine the last to e8uations:

ω drive L = RV inductor

amplitude

V resistoramplitude

.

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"here!ore i! you graph R

V inductoramplitude

V resistoramplitude

vs. ω drive) you should obtain a linear graph ith a slope e8ual

to '.

=ind ' by collecting data !or multiple dri&ing !re8uencies) maing a graph and !inding the slope..a!e your observations and graph now) /hen write your wor! and result "or L:

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Section 10:

7se your solenoid to search !or stray alternating magnetic !ields in the lab. "here are manystrange high$!re8uency electromagnetic oscillations radio a&es permeating the laboratory. 7se an

unpoered solenoid to detect the oscillating magnetic !ields o! these radio a&es in order to measure

the !re8uencies o! these signals."his is the per!ect opportunity to learn the use o! your oscilloscopes ==" !ast =ourier trans!er

math !unction. "he ==" math operation changes the time$ais to a !re8uency$ais. Fou may then

adDust the !re8uency scale using the seconds/di& nob) zoom in using the math M ==" zoom!unction) horizontally scan using the horizontal shi!t nob) and record your obser&ations belo.

Your observations:

Section 11: iscovery3

11.1. "rans!ormers in poer lines use metal contained inside their solenoid coils to help increase the

mutual inductance. *n&estigate hat inds o! metals and shapes thereo! help increase the mutualinductance in a trans!ormer. 7se to large solenoids !or this) the !unction generator and your

oscilloscope. Barious test metal pieces are in one part o! the room. "ae only one or to at a time and

put them bac immediately hen you are done i.e. share. Your discoveries:

11.2. %inusoidal electromagnetic a&es light transmitted !rom one solenoid to another can be bloced by highly conducting obDects. "his is !or the same reason that good conductors metals are

shiny) they re!lect light so it cannot pass. *n&estigate hat inds o! metals are good or poor conductors

using this e!!ect. 7se a similar setup as 11.1. >etalic sheets are in one part o! the room. "ae onlyone or to at a time and put them bac immediately hen you are done Your discoveries:

eport 5uidelines: 3rite a separate section using the labels and instructions pro&ided belo. Fou

may add diagrams and e8uations by hand to your !inal printout. (oe&er) images) tet or e8uations

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plagiarized !rom the internet are not alloedJ

• /itle A catchy title orth zero points so mae it !un.

• 5oals 3rite a 5$4 sentence paragraph stating the eperimental goals o! the lab the big

picture. o NO" state the learning goals eep it scienti!ic. ;~1$point<

• +oncepts 6 Euations ;~6$points< #e sure to rite a separate paragraph to eplain each o!

the !olloing concepts. E*&lain the following items in order:

• -plain =araday+s 'a and Ampere+s 'a.

• -plain hat causes the bac ->= in a solenoid sel!$inductance.

• -plain hy ε't &oltage across the inductor is ?0o phase$shi!ted be!ore B@ t.

• -plain hy *@ decreases hen the dri&ing !re8uency ωdri&e is increased.

• -plain ho to induce current in an unpoered circuit and the use o! 'enz+s 'a.

• -plain ho to transmit electrical poer in ires that don+t touch.

• eri&e B

insidesolenoid

= µ onI

L .

• eri&e ε L= NAd

dt .

• eri&e L solenoid= A⋅ µ o⋅ N ⋅ .

• Kompare the !re8uency dependence o! the inducti&e reactance to the capaciti&e

reactance.

• Procedure 6 esults o not rite this section. ;~0$points<

• +onclusion 3rite at least three paragraphs here you analyze and interpret the results you

obser&ed or measured based upon your pre&ious discussion o! concepts and e8uations. *t is all

right to sound repetiti&e since it is important to get your scienti!ic points across to your reader.

3rite a separate paragraph analyzing and interpreting your results !rom your open$endedeperiment. o NO" rite personal statements or !eeling about the learning process eep it

scienti!ic. ;~I$points<• 5raphs All graphs must be neatly hand$dran during class) !ill an entire sheet o! graph

paper) include a title) labeled aes) units on the aes) and the calculated line o! best !it i!applicable. ;~I$points<

o "he to graphs !rom sections 6 and ?.

• 7or!sheet thoroughly completed in class and signed by your "A. ;~C$points<

241 Solenoids

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