Matter & Interactions 2d EditionTest Question ArchivePreliminary versionChapter 22October 9, 2007The source for each problem is in a separate LATEXfile. See the file 22_problems.tex for an example ofhow to assemble these problems into an exam. Sometimes homework problems from the textbook are usedas test problems; these are not included in this collection.1Things you must knowRelationship between electric field and electric forceRelationship between magnetic field and magnetic forceElectric field of a point charge Conservation of chargeMagnetic field of a moving point charge The Superposition PrincipleOther Fundamental Concepts∆Uel= q∆V ∆V = −fiE • dl ≈−(Ex∆x + Ey∆y + Ez∆z)Φel=E • ˆndA Φmag=B • ˆndA E • ˆndA =qinside0 B • ˆndA =0|emf| = ENC• dl =dΦmagdt B • dl = µ0Iinside pathSpecific ResultsE due to uniformly charged spherical shell: outside like point charge; inside zeroEdipole,axis≈14π02qsr3(on axis, r  s)Edipole,⊥≈14π0qsr3(on ⊥ axis, r  s)Erod=14π0Qrr2+(L/2)2(r ⊥ from center) p = qs electric dipole momentErod≈14π02Q/Lr(if r  L)Ering=14π0qz(z2+ R2)3/2(z along axis)Edisk=Q/A201 −z(z2+ R2)1/2(z along axis)Edisk≈Q/A201 −zR≈Q/A20(if z  R)Ecapacitor≈Q/A0(+Q and −Q disks)Efringe≈Q/A0s2Rjust outside capacitor∆B =µ04πI∆l × rr2(short wire) ∆F = I∆l ×BBwire=µ04πLIrr2+(L/2)2≈µ04π2Ir(r  L)Bloop=µ04π2IπR2(z2+ R2)3/2≈µ04π2IπR2z3(on axis, z  R) µ = IA = IπR2Bdipole,axis≈µ04π2µr3(on axis, r  s)Bdipole,⊥≈µ04πµr3(on ⊥ axis, r  s)i = nA¯vI= |q| nA¯v ¯v = uEσ = |q| nu J =IA= σE R =LσAEdielectric=EappliedK∆V =q4π01rf−1ridue to a point chargeQ = C |∆V | Power = I∆VI=|∆V |R(ohmic resistor)K ≈12mv2if v  c circular motion:dpdt⊥=|v|R|p|≈mv2R2Constant Symbol Approximate ValueSpeed of light c 3 × 108m/sGravitational constant G 6.7 × 10−11N · m2/kg2Approx. grav field near Earth’s surface g 9.8N/kgElectron mass me9 × 10−31kgProton mass mp1.7 × 10−27kgNeutron mass mn1.7 × 10−27kgElectric constant14π09 × 109N · m2/C2Epsilon-zero 08.85 × 10−12N · m2/C2Magnetic constantµ04π1 × 10−7T · m/AMu-zero µ04π × 10−7T · m/AProton charge e 1.6 × 10−19CElectron volt 1 eV 1.6 × 10−19JAvogadro’s number NA6.02 × 1023molecules/moleAtomic radius Ra≈ 1 × 10−10mProton radius Rp≈ 1 × 10−15mE to ionize air Eionize≈ 3 × 106V/mBEarth(horizontal component) BEarth≈ 2 × 10−5T3022-001A magnet, oriented as shown, with magnetic moment µ moves at speed v toward a coil of radius R,withN turns, oriented as shown in the diagram. (Note that θ<90◦.) The coil is connected to a voltmeter.NSto + inputof voltmeterto – inputof voltmetervN turnsradius Rxθ(a) What is the sign of the voltmeter reading? (Remember that a voltmeter reads ”+” if the higher voltageis connected to the ”+” terminal of the voltmeter.) Explain briefly.(b) At the instant when the magnet is a distance x from the center of the coil, what is the magnitude ofthe voltmeter reading? State what approximations or simplifying assumptions you make.4022-002The north pole of a bar magnet points toward a thin circular coil of wire containing 40 turns. The magnetis moved away from the coil. At time t = 0, the center of the bar magnet is 9 cm from the center of thecoil, and 0.05 seconds later the center of the magnet is 13 cm from the center of the coil. Assume that atany given time the magnetic field produced by the magnet is nearly uniform over the area enclosed by theloop. Note that the diagram is not to scale.NNSr = 0.06m40 turnsend view(a) At the location of the coil, draw and label arrows representing the following vector quan- tities:Bi,Bf,∆B∆t, −∆B∆t. The relative lengths of the arrows must be correct.(b) Viewed from the right side (from the side opposite the bar magnet), does the induced current runclockwise or counterclockwise in the circular coil?5022-004A conventional current I runs through a 500 turn coil of radius 9 cm in the direction shown in the diagram.Initially the current in the coil is constant and is 3.5 amperes. A single loop of copper wire of radius 4 cmis placed 5 m from the coil. Both loop and coil are stationary.Power supplycoilloopPxyzI(a) In this initial state (constant current in coil), what is the direction of the magnetic field at the centerof the copper loop, due to the current in the coil?(b) In this initial state, what is the direction of the electric field at location P inside the copper loop?(c) What is the absolute value of the magnetic flux in the copper loop at this initial time t1? Show yourwork.(problem continued on next page)6(d) Now the power supply is adjusted so the current in the coil decreases and 0.08 s later the current is1.2 amperes. What is the magnitude of the induced emf in the copper loop? Show your work.(e) Draw an arrow on the diagram indicating the direction of the electric field in the copper loop at locationP . Explain briefly how you determined the direction, using words and/or arrows.7022-005A conventional current I runs through a 750 turn coil of radius 7 cm in the direction shown in the diagram.Initially the current in the coil is constant and is 2.1 amperes. A single loop of copper wire of radius 3.5cm is placed 6.2 m from the coil. Both loop and coil are stationary and their axes on the same straightline.Power supplycoilloopBcoilPxyz(a) What is the direction of the current in the coil when viewed from the left of the coil?(b) In this initial state, what is the direction of the electric field at location P inside the copper loop?(c) What is the absolute value of the magnetic flux in the copper loop at this initial time t1? Show yourwork.(problem continued on next page)8(d) Now the power supply is adjusted so the current in the coil increases and 0.12 s later the current is4.8 amperes. What is the magnitude of the induced emf in the copper loop? Show your work.(e) Draw an arrow on the diagram