HW #5 Hints. Today. HW #5 Hints. HW #5 Hints. Announcements:

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Amy Barnett
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1 Today HW #5 Hints Announcements: HW and Exta cedit #3 due 2/25 HW hints + Recap the 2nd law of themodynamics Electic and Magnetic Foces and thei unification the Foce Field concept -1-1) The speed at D is than the speed at A 2) The speed at D is than the speed at C 3) The acceleation at D is zeo, tue o false 4) The acceleation at A points in the. Diection a) +x b) - x c) +y d) -y e) none, it is zeo Hint: Questions 1,2 use Consevation of enegy Hint: think of cicula Motion fo? s 3,4-2- HW #5 Hints HW #5 Hints Consevation of enegy E A = E B = E C = E D D Consevation of enegy E A = E B = E C = E D A 1) The speed at D is than the speed at A 1) The speed at D is than the speed at A At initial point B, ALL enegy is potential enegy E B = mgh B At point A, we have a mix of PE and KE E A = mgh A + 1/2 mv A 2 At point D, we have a mix of PE and KE E D = mgh D + 1/2mv D 2-3- Speed at A is > speed at D (common sense!) -4-

2 HW #5 Hints Think of cicula motion to answe Questions about Acceleation at A and D Let s illustate this with a familia example -- the moon Obiting the eath in a cicula obit. HW # 5 Hints Is the moon expeiencing Acceleation? YES, since The diection of velocity Is changing at each point. What diection is the Acceleation? It is in The same diection as the Foce that is causing it (I.e., towads the cente Of the ciclula obit) HW #5 Hints Enegy and Entopy - Pendulum Example Think of cicula motion to answe Questions about Acceleation at A and D Enegy At these points, the wie foms a small segment of A cicula path. We leaned that in cicula motion, An object is being acceleated, and the diection of Acceleation is towads the cente of the cicle. -7- If thee is no fiction, the pendulum swings foeve, always following the same tajectoy. The figue shows how the enegy is split into Kinetic And Potential enegy at each point in the tajectoy. The themal enegy (heat) is lost -8-

3 Enegy Enegy and Entopy - Pendulum Example The themal enegy (heat) is lost -9- Entopy Entopy is a measue of the numbe of ways a system can be aanged. S = k B ln(# of aangements) S = Heat/T themal enegy goes towad inceasing the entopy Second Law of Themodynamics The entopy of a closed system always inceases. As the pendulum swings useful enegy is lost to inceasing the andom motion of the ai and pivot (heat) 2nd law => Thee is no way to ecollect the themal enegy and make the pendulum swing highe as in the fictionless case Coin Toss Example Suppose we have 10 coins: HHHHHHHHHH S = k ln(1) = 0 Heads Numbe of ways Entopy (J/K) * Why does time always move in one diection? The Univese was ceated with vey low entopy. Much too low fo its size. It is like the Univese stated with all heads. Hence, eveything in the Univese moves towad eaching the coect amount of entopy. It is vey impobable to go the othe way. In this case vey means so impobably that it neve happens. Time has a diection because going back in time would imply the entopy could be deceased. That is vey impobable. The Univese tends towad inceasing entopy. -12-

A new foce Magnetic foce Magnets in diffeent contexts Cetain objects in natue have magnetic poles They always come in pais, noth and south poles.

monopoles ) have been seen CC data stip Tansfomes to aise/lowe electic potential in tansmission line High speed maglev tains Electic motos Cycloton

-13- and countless othes MRI Nothen lights -14- What causes the magnetic foce?

Cuent is the flow of chage (electons) in a wie, simila to wate flowing in a pipe.

4 A new foce Magnetic foce Magnets in diffeent contexts Cetain objects in natue have magnetic poles They always come in pais, noth and south poles. Like poles epel, unlike poles attact Even if you cut the magnet in half, they still come in pais (N & S) It is a geat mystey why no single poles ( monopoles ) have been seen CC data stip Tansfomes to aise/lowe electic potential in tansmission line High speed maglev tains Electic motos Cycloton paticle Acceleato next doo If you see one, book you ticket to Stockholm to pick up you Nobel Pize! -13- and countless othes MRI Nothen lights -14- What causes the magnetic foce? The coespondence of a loop of cuent and magnet Moving chage ( cuent ) causes a magnetic field. Cuent is the flow of chage (electons) in a wie, simila to wate flowing in a pipe. Lage scale cuent in the Eath is due to the liquid coe of the eath and its otation give the Eath a magnetic field. The exact natue is not known. The Eath s changing magnetic field: Magnets have an intenal stuctue whee the motion of the electons ceates small egions with cuents. Cuents ceate magnetic fields (see geen aows) -16-

How to Build a Magnet Foce Fields: A distubance of space Moving chage ceates a magnetic field Is it possible to

-17- Foce Fields: A distubance of space -18- Foce Fields: A distubance of space The eath s gavitational field

Seeing a magnetic field lines with ion filings The existence of a field means that if an appopiate object is

5 How to Build a Magnet Foce Fields: A distubance of space Moving chage ceates a magnetic field Is it possible to exet a foce on something fom a distance? At fist glance, it might seem not, but then how does gavity wok? Ditto fo electical/magnetic foces. We call the thing that tansmits the foce a foce field; it is not an object but athe a popety of space itself Foce Fields: A distubance of space -18- Foce Fields: A distubance of space The eath s gavitational field suounds the eath; it would be thee even if the moon wasn t. Seeing a magnetic field lines with ion filings The existence of a field means that if an appopiate object is neaby, it will expeience a foce. Electomagnetism woks the same way; thee ae electic and magnetic fields. An electic field will exet a foce on a chage, and a magnetic field will exet a foce on a moving chage Cuent in a wie ceates a Magnetic field -20-

The Eath s magnetic field: How a compass woks Magnetic field lines point fom Noth magnetic poles -21to South magnetic poles.

Thee ae fou equations that give the elationship. These ae Maxwell s Equations.

The electic foce is what pevents us fom falling to the cente of the Eath! -23- Eath s Magnetic Field and Potection fom the sun We d be dead without it!

6 The Eath s magnetic field: How a compass woks Magnetic field lines point fom Noth magnetic poles -21to South magnetic poles. Unifying Electicity and Magnetism The magnetic foce and the electic foce ae elated. They ae two manifestations of what we call the electomagnetic foce. Thee ae fou equations that give the elationship. These ae Maxwell s Equations. Chage ceates the electic foce Moving chage ceates the magnetic foce Maxwell s equations unified the electic and magnetic foces. The electic foce is what pevents us fom falling to the cente of the Eath! -23- Eath s Magnetic Field and Potection fom the sun We d be dead without it! -22- Maxwell s Equations Unify Electicity/Magnetism Chage makes an electic field. "! E = 4&' 4& 1 #E Moving chage makes a magnetic "%B = J+ field. c c #t Changing magnetic field makes an 1 #B electic field ( Faaday s Law ) "%E = $ c #t Magnets always have a noth and a "!B = 0 south pole The equations pedict the existence of an wave that tavels with speed c, the speed of light. -24-

Faaday s law is behind the whole industy of electic powe geneation. If a powe souce can be made to tun a shaft in a magnetic field, electicity will be poduced.

7 Faaday s law is behind the whole industy of electic powe geneation. If a powe souce can be made to tun a shaft in a magnetic field, electicity will be poduced. Electicity geneation -25- Electic Chage Electic chage is a popety of matte. It is measued in Coulombs The chage on one electon is 1.602E-19 C How many electons in a chage of 1 C? Total Chage 1C #Electons = = Chage 1.602E! 19 C electon electon #Electons = 6.215E Electic and Magnetic Fields If we move a test chage, q, (o magnet) in the vicinity of anothe chage (o magnet) we can make a map of the foce. Define: Electic field E = F/q Electic field is a vecto. Its units ae N/C o V/m (volts/mete). It points in the diection of the foce. Once we know the electic field we can calculate the foce: F=qE F = electic field times chage of the object in the field Which is undelying eality, the foce o the field? -27- Samples Electic field lines point away fom positive chage and towad negative chage. Chage geneates an electic field. -28-

The Stength of the Electic Field Example Electic potential SI unit is the Volt

x The minus sign means that electic fields point fom + to chage.

-30- Lightning Sample Poblem What is the magnitude of the electic field at: 0.

Potential diffeence of 100 MV is developed between cloud and gound.

8 The Stength of the Electic Field Example Electic potential SI unit is the Volt (V) Electic field is ate of change of potential! V E = "! x The minus sign means that electic fields point fom + to chage V -20 V The electic potential is the same eveywhee on a conducto Lightning Sample Poblem What is the magnitude of the electic field at: 0.5 m? 1.5 m? 3.0 m? Potential diffeence of 100 MV is developed between cloud and gound. In the bolt about 5 C of chage ae tansfeed (on aveage) The field is 0 V/m at 0.5 m and 3.0 m since the slope is zeo. " V ( 100V! 0V ) V E( at 1.5m) = = = 100 " x 2m! 1m ( ) m -32-

9 A visual pictue Electic Potential Electic fields and potential - Negative chage makes a valley. Positive chage makes a hill +q Steep slope means a lage foce In equilibium the electic field in a metal conducto is zeo. This means that inside a metal the electic potential is flat, like the flat top of a table. Sitting inside a metal cage is like sitting on top of a lage, flat table. As long as you ae in the cente, thee is no dange of falling off. This is why being in a ca duing a thunde stom is elatively safe Electic Field Example Q = 0.5 µc = 0.5x10-6 C What is the magnitude of the electic foce on Q? F = qe F = 0.5E-6C x 40 N/C = 20E-6 N Not asked fo, but the diection is +, to the ight. Electic Field E = -!V/!x =-(50V-90V)/1m= 40 V/m + means to the ight in this case -35-

A new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet.

A new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet. Today A new foce Magnetic foce Announcements HW#6 and HW#7 ae both due Wednesday Mach 18th. Thanks to my being WAY behind schedule, you 2nd exam will be a take-home exam! Stay tuned fo details Even if