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# Principles of Electricity and Magnetism 1 PHYS 3310

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This 68 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 3310 at University of Colorado at Boulder taught by Steven Pollock in Fall. Since its upload, it has received 15 views. For similar materials see /class/232091/phys-3310-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.

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Date Created: 10/30/15

CHAPTER6 MAGNEWZAWON Griffiths argues that the torque on a magnetic dipole in a B field is fzmxB How will a small current loop line up if the B field points uniformly up the page fA mff C in B T i 62 Griffiths argues that the force on a magnetic dipole in a B field isF V 1B If the dipole m points in the z direction what can you say about B if I tell you the force is in the x direction A B simply points in the x direction B B2 must depend on x C Bz must depend on 2 D Bx must depend on x E Bx must depend on 2 63 A solid cylinder has uniform magnetization M throughout the volume in the z direction as shown Where do bound currents show up A Everywhere throughout t volume and on all surface B Volume only not surface C Topbottom surface only DSide rounded surface 0 E All surfaces but not volu 64 A1tR2 L M C 27tR M A solid cylinder has uniform magnetization M throughout the volume in the x direction as shown What39s the magnitude of the total magnetic dipole moment of the c linder B 21tRLM DnR 2M E Something else it39s more complicated 65 A solid cylinder has uniform magnetization M throughout the volume in the x direction as shown Where do bound currents show up A Topbottom surface only BSide rounded surface 0 C Everywhere D Topbottom and parts of but not all of side surfac but not in the volume E Something differentothe combination To discuss A solid cylinder has uniform magnetization M throughout the volume in the z direction as shown What will the B field look like Consider if the cylinder is tall short and fat separately 66 A sphere has uniform magnetization M in the z direction Which formula is correct for this surface current A M sine B M sine g5 C M cose D Moose g5 E None of these Coming up first today Write down by yourself without book or notes or collaboration yet what you remember about electric Polarization P and all related concepts and formulas we39ve worked with 7 A small chunk of material the tan cube is placed above a solenoid t magnetizes weakly as shown by small arrows inside What kind of material must the cube be m A Dielectric B Conductor L C DiamagnetIc D ParamagnetIc E Ferromagnetic g7 Predict the results of the following experiment a paramagnetic bar and a diamagnetic bar are pushed inside of a solenoid a The paramagnet is pushed out the diamagnetis suc ed in b The diamagnet is pushed out the paramagnet is suc ed in c Both are sucked in but with different force d Both are pushed out but with different force AUXILIARY FIELD H 68 A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction We know B will be CCW as viewed from above Right What about H and M inside the cylinder A Both are CCW B Both are CW 0 C H is CCW but M is CW D H is cw M is ccw E A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction We know B will be CCW as viewed from above Right What about H and M inside the cylinder LINEAR AND NONLINEAR MEDIA 69 A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction What is the direction of the bound volume current A JB points parallel to l B JB points antiparallel to l C Othernot sure A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction What is the direction of the bound volume current A JB points parallel to l A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction What is the direction of the bound surface current A KI3 points parallel to l B KI3 points antiparallel to l C Othernot sure A very long aluminum paramagnetic rod carries a uniformly distributed current I along the 2 direction What is the direction of the bound volume current KI3 points antiparallel to 610 A large chunk of paramagnetic material xmgt0 has a uniform eld BO throughout its interior We cut out a cylindrical hole very skinny very 39 ii ii What is B at the center of that hole A B0 B more than B0 C less than B0 D S10 A large chunk of paramagnetic material xmgt0 has a uniform eld BO throughout its interior We cut out a waferlike hole very wide very shonD TTTTBOT TTTTt What is B at the center of that hole A B0 B more than BO C less than B0 D 611 A sphere with a spherical cavity inside it is made of a material with very large positive Xm It is placed in a region of uniform B field Which figure best shows the resulting B field lines 5 E E None of these can be even remotely correct 611 Mumetal 75 nickel 15 iron plus copper and molybdenum acts as a sort of magnetic shield there is no perfect Faraday cage effect for magnetism why not A 512 A superconducting ring sits above a strong permanent magnet N side up If you drop the ring which way will current flow as viewed from above and what kind of force will the ring feel A CWrepulsive CWattractive COWrepulsive COWattractive No net current will flowno net force I39I39IUOUJ To think aboutdiscuss mber Lenz law What does it say about this situation What will the resulting motion of the ring look like What if you dropped a magnet onto the ring instead of dropping the ring onto the magnet 613 Inside a hollow solenoid BB p nl so HHnnl If the solenoid is lled with a paramagnetic material what is B inside ABD B a little more than BEl C a lot more than BEl D a little less than BEl E a lot less than BEl 614 Inside a hollow solenoid B l HH n If the solenoid is lled with iron what is H inside 3 AHu B a little more than HEl C a lot more than HEl D a little less than HEl E a lot less than HEl BOUNDARYVALUE PROBLEMS 611 I have a boundary sheet and would like to learn about the change or continuity of Hparallel across the boundary Habove u H above Am I going to need to know about mVxH BVOH C 611 I have a boundary sheet and would like to learn about the change or continuity of Hperp across the boundary H Labove 39 Am I going to need to know about mVxH B V 0H C CHAPTER 4 Electrostatics in Matter Polarizationdielectrics Field of polarized objectbound charge Electric displacement Linear dielectrics POLARIZATION 41 The cube below side a has uniform polarization P0 which points in the z direction What is the total dipole moment of this cube Azero 41 The sphere below radius a has uniform alt polarization P0 which points in the z direction What is the total dipole moment of this sphere A zero complicated 42 You put a conducting sphere in a uniform Efield How do you expect the surface charge to depend on the polar angle 0 r r a Constant b cose c sine d Nothing simple it will have to be an infinite series of sin s and cos s with coefficients Now what if the sphere is a dielectric How do you expect the bound surface charge to depend on the polar angle 0 V i 7 a Nothing simple it will have to be an infinite series of sin s and cos s with coefficients FIELD OF POLARIZED OBJECT IIIII llllll 39393939 39393939 39393939 39393939 39393939 uuuuuu IIIII uuuuuu llllll llllll IIIII IIIII IIIII uunuuu 43 In the following case is the bound surface and volume charge zero or nonzero Aob 0 pb 0 Bob 72 0 pb 0 Cob 0 pb0 Dob 7t 0 pb0 TM 636 TM 6363 TM Physical dipoles idealized dipoles 43 In the following case is the bound surface and volume charge zero or nonzero COO TTT 999 T T T A39Gb0lpb 0 T T T Bob 72 O pb 0 Physical dipoles idealized dipoles Cob O pb0 Dob 7t 0 pb0 41 The sphere below radius a has uniform alt polarization PO which points in the z direction What is the total dipole moment of this sphere 39 A zero B PO a3 C 47ta3 PO3 D Po E None of thesemust be mor complicated 44A dielectric slab top area A height h has been polarized with PP0 in the 2 direction What is the surface charge density 6b on the bottom surface AO i Poi In your own words define what we mean by quotfree chargequot and quotbound chargequot ELECTRIC DISPLACEMENT 45 We introduced quotElectric Displacementquot or quotDquot field D 80E P If you put a dielectric in an external field Eext it polarizes adding a new field Einduced from the bound Charges These superpose making a total field Etot Which of these three E fields is the quotEquot in the formula for D above AEext B Einduced CEtot 7 We define D 80E P With all ltJJgtDO dA Qfree enclosed A point charge q is placed at the center of a dielectric sphere radius R There are no other free charges anywhere What is Dr A q4 7 r2 everywhere B q4 7 so r2 everywhere C Answer A above for rltR but answer B above for rgtR D None of the above it39s more complicated E We need more info to answer 46 An ideal large capacitor has charge Q A neutral dielectric is inserted into the gap and of course it will polarize We want to find D everywhere i D 0 E P a a m ltquotgt M QM 39 39 a a 0 0 E39dA Q80 Which equation would you go to first Ai B ii C iii D Your call more than 1 of these would work E Can39t solve unless know the dielectric is linear 46 An ideal large capacitor has charge Q b A neutral dielectric is inserted into the gap and of course it will polarize We want to find E everywhere i D 80 E P 39 39 c c m ltquotgt M QM 39 39 a a 0 0 EMA Q80 Which equation would you go to first Ai B ii C iii D Your call more than 1 of these would work E Can39t solve unless know the dielectric is linear 46 An ideal large capacitor has charge Q C A neutral lineardielectric is inserted into the gap with given dielectric constant We want to find D in the dielectric odg eree When drawing the Gaussian pillbox shown what is ereeenclosed A SA B oBA C 6A oBA D SA 6B A E Something else 46 An ideal large capacitor has charge Q A neutral lineardielectric is inserted into the gap with given dielectric constant Now that we have D in the dielectric What is E inside Q the dielectric 539 6 BEDe CED80 DEDeO E Not so simple Need another method 46 An ideal large capacitor has charge Q 9 A neutral lineardielectric is inserted into the gap with given dielectric constant Now that we have D in the dielectric What is E in that small gap above the dielectric 08 E CED80 DEDeO E Not so simple Need another method 46 An ideal large capacitor has charge Q f A neutral lineardielectric is inserted into the gap with given dielectric constant Where is E discontinuous i near the free charges E on the plates ii near the bound charges on the dielectric surface Ai only B ii only C both i and ii but nowhere else D both i and ii but also other places E none of theseother 46 An ideal large capacitor has charge Q 9 A neutral lineardielectric is inserted into the gap with given dielectric constant Where is D discontinuous i near the free charges E on the plates ii near the bound charges on the dielectric surface Ai only B ii only C both i and ii but nowhere else D both i and ii but also other places E none of theseother 4397 A point charge q is placed at the center of a dielectric sphere radius R There are no other free charges anywhere but the sphere polarizes producing bound charge in the sphere Which charges contribute to the total E field inside the dielectric A q only B q and the bound charges C bound charges only D It depends on whether the material is a linear dielectric or not 7 A point charge q is placed at the center of a dielectric sphere radius R There are no other free charges anywhere but the sphere polarizes producing bound charge in the sphere Which charges contribute to calculating D inside the dielectric A q only B q and the bound charges C bound charges only D It depends on whether the material is a linear dielectric or not A point charge q is placed at the center of a dielectric sphere radius R There are no other free charges anywhere What is Dr 4 C A q4 7 r2 everywhere B q4 7 so r2 everywhere C lt39s answer A above for rltR but answer B above for rgtR D None of the above it39s more complicated E We need more info to answer eg is it a linear dielectric 4398 An infinitely long solid nonconducting dielectric rod has been injected quotdopedquot with a fixed known charge distribution ps The material responds polarizing internally When computing D in the rod do you treat this ps as the quotfree chargesquot or quotbound chargesquot or neither A quotfree chargequot B quotbound chargequot C Neither of these a given ps is already some combination D ps LINEAR DIELECTRICS Can a dielectric material have free charges inside it andor on its surface A No any charges in or on a dielectric are by de nition bound charges B Yes but they can ONLY be inside not on the surface C Yes but they can ONLY be on the surface not inside D Yes 9 Is the polarization of a dielectric always proportional to the Electric field E A Yes if by quotEquot you mean quotEexterna B Yes if by quotEquot you mean quotEtotalquot C Yes if by quotEquot you mean quotEinducedquot D No it doesn39t have to be proportional 8 g What IS 8 1n a vacuum r 80 a 1 b 0 c in nity 1 not de ned e None of the above 8 g What IS 3r in copper 80 a 1 b 0 c in nity or extremely large 1 not de ned e None of the above 8 8 What is 8 in water 80 a 1 b 0 c in nity 1 not de ned e None of the above BOUNDARY VALUE PROBLEMS WITH DIELECTRICS You have a straight boundary between two linear dielectric materials ar has one value above another below the boundary There are no free charges in the regions considered What is continuous across the boundary i Eparallel ii Eperpendicular iii Dparallel iv Dperpendicular A i and iii B ii and iv C i and ii D iii and iv E Some other combination 410 You have a boundary between two linear dielectric materials ar has one value above another below the boundary There are no free charges in the regions considered Which formula will voltage satisfy at the boundary A aV aV Ofree av aV 0baund an out an in 80 an out an in 80 8V 8V Ofree 3V 3V I I 0 C 8W an M m an in 80 D 80m an m 8m an M E None of these or MORE than one 210 You have a boundary between two linear dielectric materials ar has one value above another below the boundary There are no free charges in the regions considered Which formula will voltage satisfy at the boundary 0 AV VO BVt V m out In W m 80 C 8m V 8m V 0 D am e VI 0 E None of these or MORE than one Boundary Value Exercise 0 A multistep question 0 For a dielectric sphere in an electric eld E0 0 l draw sketch including E and charge sigmabound 2 write down boundary conditions 0 3 What equation will you use to solve E inside ie what solution to Laplace 4 Tell me the steps you will go through without doing calculation 0 5 How would you eXpect E inside to depend on E0 FORCE AND ENERGY 411 We argued that C goes UP by a factor of er if you fill a capacitor with dielectric What happens to the stored energy of a capacitor if it s filled with a dielectric A It goes up B It goes down C It is unchanged DThe answer depends on what else is held fixed V Q 412 If we push this conductor inside the isolated capacitor will it be drawn into the capacitor or repelled O39 METAL 0 A It gets sucked into the capacitor B It gets pushed out from the capacitor C just don t know 412 b If we push this conductor inside the isolated capacitor will it be drawn into the capacitor or repelled O39 DIELECTRIC 0 A It gets sucked into the capacitor B It gets pushed out from the capacitor C just don t know 330 raw I 51even FOHO R G C M 39 E DU cf s39ffiij WWWcoo 21OOEDo jS cs fgjss3m EX D 5 km a K Tue 4 1 9153 MW Due everj Wei 5 of thus MM 7L3 week 190 gyf w 1 vusgonj He 158550 5 Fr 5 m Svem m r M H S 7 735 70 cm e zol w Rg gnj 4 weal AJVer Semez 7 X5 quot39 XV 3A Any In of I 3 you hen 1390 QUICK Prcte 5 570 me 61 s welcome 4 7 cl39fxfr f J f lm1 s TLIS Course 61500 E I gg 9 unk Low 75 locq39rion fern73 705 It vainum I 9 5435 f r inch of exfcrk nc J fl39jsnj 39 quot Haiti 0 MSWLCMQ IICq Plde como lave neSj 39 9 d ificmwn39 M 2quot reIQVIVI HjJ ficlcQ T eory quotDeep questionsquot Is Coulomb s force law valid for all separation distances Is it valid for r0 What is the physics origin of the r 2 dependence of Coulomb s force law What is the physics origin of the 180 dependence of Coulomb s force law What is the physics origin of the 1411 factor in Coulomb s force law 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