Final&review 1
Practice(final(Q2 2. [7 pts.] The figure shows two charges, q L and q R, of opposite sign. Charge q L has greater magnitude than charge q R. In which of the regions X (left of q L ), Y (between q L and q R ), Z (right of q R )will there be a point at which the net electric field due to these two charges is zero? (a) Only region X q L q R X Y Z (b) Only region Y (c) Only region Z (d) Only regions X and Z (e) Need more information INTRODUCTION 2
Practice(final(Q2(answer Only%region%Z! " = $ % & '*, "- () Electric%field%points%towards%a%positively%charged%particle,% and%away%from%a%negatively%charged%particle. For%the%net%electric%field%to%be%zero,%the%electric%field%from% each%charge%must%point%in%opposite%directions.%so%the%region% between%charges%is%ruled%out. The%magnitude%of%electric%field%linearly%depends%on%the% charge,%so%the%left%charge%creates%a%stronger%electric%field%for% a%given%distance%from%it. q L q R X Y Z If%q L was%a%negative%charge q L q R X Y Z If%q L was%a%positive%charge INTRODUCTION 3
Practice(final(Q4 Use the diagram to the right for the following two questions. An electric dipole consists of a 3.00 10 6 C charge and a 3.00 10 6 C charge separated by 1.20 10 3 m. The dipole is placed in a uniform electric field of magnitude 525 N/C oriented as shown in the figure. 3 μc 140 4. [7 pts.] What is the magnitude of the net torque this field exerts on the dipole? -3 μc (a) 0.61 10 6 N m (b) 1.21 10 6 N m (c) 1.45 10 6 N m (d) 1.89 10 6 N m (e) 3.34 10 6 N m INTRODUCTION 4
Practice(final(Q4(answer Use the diagram to the right for the following two questions. An electric dipole consists of a 3.00 10 6 C charge and a 3.00 10 6 C charge separated by 1.20 10 3 m. The dipole is placed in a uniform electric field of magnitude 525 N/C oriented as shown in the figure. 3 μc 140 4. [7 pts.] What is the magnitude of the net torque this field exerts on the dipole? -3 μc # = % ' # = %' sin + =,-' sin + = 3.00 10 23 C 1.20 10 26 m 525 N C sin 140 = 1.21 10 23 N = m INTRODUCTION 5
Practice(final(Q5 Use the diagram to the right for the following two questions. An electric dipole consists of a 3.00 10 6 C charge and a 3.00 10 6 C charge separated by 1.20 10 3 m. The dipole is placed in a uniform electric field of magnitude 525 N/C oriented as shown in the figure. 3 μc 140-3 μc 5. [7 pts.] How much work does the electric field do on the dipole as it rotates clockwise by 140 from the orientation shown? (a) 0.72 10 7 J (b) 1.45 10 6 J (c) 1.67 10 6 J (d) 1.89 10 6 J (e) 3.34 10 6 J INTRODUCTION 6
Practice(final(Q5(answer Use the diagram to the right for the following two questions. An electric dipole consists of a 3.00 10 6 C charge and a 3.00 10 6 C charge separated by 1.20 10 3 m. The dipole is placed in a uniform electric field of magnitude 525 N/C oriented as shown in the figure. 3 μc 140-3 μc 5. [7 pts.] How much work does the electric field do on the dipole as it rotates clockwise by 140 from the orientation shown? The$dipole$rotates$about$its$center.$The$the$component$of$the$displacement$of$each$charge$in$ the$direction$of$the$the$electric$force$on$it$is$! 1 + cos 180 140. " So$the$work$done$by$the$electric$force$is$- = / 1 1 0 + /! 2 1 + cos 180 140 = " 245! 1 + cos 180 140 = 3.00 " 1029 C 525 N C 1.20 10 2> m [ 1 + cos( 180 140 )] = 3.34 10 29 J INTRODUCTION 7
Practice(final(Q6 6. [7 pts.] What is the power dissipated by the 1.0 resistor? (a) 0 W (b) 2 W (c) 4 W (d) 8 W (e) 14 W 2.0 A 2.0 Ω 7.0 V 3.0 V 1.0 Ω INTRODUCTION 8
Practice(final(Q6(answer 6. [7 pts.] What is the power dissipated by the 1.0 resistor? (a) 0 W 2.0 A 2.0 Ω (b) 2 W (c) 4 W (d) 8 W 7.0 V 1.0 Ω 3.0 V (e) 14 W The$current$flowing$through$the$1.03Ω resistor$is$2.0$a. " = $ % & = 2.0 A % 1.0 Ω = 4 W INTRODUCTION 9
Practice(final(Q9 As shown, an observer in the earth frame (E) sees a stationary wire with no net charge. Electrons within the wire are moving to the right at speed v, so that there is a current I to the left. Below the wire is a positive charge q also moving to the right at a speed of v. Another observer (M) is moving to the right at a speed of v with respect to the earth frame. 9. [7 pts.] What is the type and direction of the force, if any, on q as observed in the M frame? (a) There is an electric force on q directed up the page. (b) There is an electric force on q directed down the page. (c) There is a magnetic force on q directed up the page. (d) There is a magnetic force on q directed down the page. (e) There is no force on q. INTRODUCTION 10
Practice(final(Q9(answer There%is%an%electric%force%on%q%directed%down%the%page. INTRODUCTION 11
Practice(final(Q10 As shown, an observer in the earth frame (E) sees a stationary wire with no net charge. Electrons within the wire are moving to the right at speed v, so that there is a current I to the left. Below the wire is a positive charge q also moving to the right at a speed of v. Another observer (M) is moving to the right at a speed of v with respect to the earth frame. 10. [7 pts.] If the charge density of positive charges measured in the E frame is E, what is the charge density of positive charges measured in the M frame? (a) (b) (c) (d) (e) E r r E E E 1 v2 c 2 0 E 1+ v2 c 2 0 q 1 v 2 c 2 0 q 1+ v2 c 2 0 INTRODUCTION 12
Practice(final(Q10(answer 10. [7 pts.] If the charge density of positive charges measured in the E frame is E, what is the charge density of positive charges measured in the M frame? Due$to$the$length$contraction,$the$distance$between$the$ adjacent$positive$charges$are$smaller$in$the$m$frame$than$in$ the$e$frame.! " = $! % =! % / 1 )* +, * INTRODUCTION 13
Practice(final(Q12 In two di erent cases, a point P is shown next to a long wire. Two Ampèrian loops, one circular and one square, pass through point P and enclose each wire. 12. [7 pts.] Suppose you knew that each wire carries a current I toward the top of the page. Could you use either of the Ampèrian loops to determine the magnetic field at point P? (a) Yes, you could use the circular loop. (b) Yes, you could use the square loop. (c) Yes, you could use both loops. (d) No, you could not use either loop. INTRODUCTION 14
Practice(final(Q12(answer In two di erent cases, a point P is shown next to a long wire. Two Ampèrian loops, one circular and one square, pass through point P and enclose each wire. 12. [7 pts.] Suppose you knew that each wire carries a current I toward the top of the page. Could you use either of the Ampèrian loops to determine the magnetic field at point P? (a) Yes, you could use the circular loop. From%the%cylindrical%symmetry,%! is%constant%along%the%circular%path,%but%not%the%square%path. Since%B%field%lines%are%continuous,%and%from%the%cylindrical%symmetry,%we%can%deduce%that%the%B% lines%form%circles%around%the%wire.%! # % for%the%circular%path. For%the%circular%path%! # % =!#% =! #% =!2*+ =, -. INTRODUCTION 15
Potential)drops)across)bulbs The$bulbs$in$this$circuits$are$identical$and$ideal.$The$battery$has$an$emf of$e.$rank$the$ magnitudes$of$potential$difference$across$the$bulbs$and$e,$smallest$first. INTRODUCTION 16
Potential)drops)across)bulbs)answer The$bulbs$in$this$circuits$are$identical$and$ideal.$The$battery$has$an$emf of$e.$rank$the$ magnitudes$of$potential$difference$across$the$bulbs$and$e,$smallest$first. Bulb$A$is$connected$in$parallel$to$the$battery,$so$" # = E. The$combination$of$Bulb$B$and$C$is$connected$in$parallel$to$the$battery,$so$" % + " ' = E,$and$ since$bulb$b$and$c$are$identical,$" % = " ' < E. " % = " ' < E = " # INTRODUCTION 17
Currents(in(bulbs The$bulbs$in$this$circuits$are$identical$and$ideal.$The$battery$has$an$emf of$e.$rank$the$the$ amount$of$currents$in$the$bulbs,$smallest$first. INTRODUCTION 18
Currents(in(bulbs(answer The$bulbs$in$this$circuits$are$identical$and$ideal.$The$battery$has$an$emf of$e.$rank$the$the$ amount$of$currents$in$the$bulbs,$smallest$first. Since$Bulb$B$and$C$are$connected$in$series,$they$have$same$amount$of$current$flowing$through$ them,$" # = " %.$ The$branch$with$Bulb$B$and$C$has$a$equivalent$resistance$that$is$twice$the$resistance$of$Bulb$A.$ So$Bulb$A$has$twice$the$current$as$Bulb$B$or$C$since$both$branches$have$the$same$potential$ difference,$e. " # = " % < " ' INTRODUCTION 19
Induction Conducting*parallel*rails*with*negligible*resistance*are*connected*by*a*resistor*with*a*resistance* of*! = 10 Ω,*and*a*conducting*rod*is*free*to*slide*on*the*rails*as*shown.*An*external*uniform* constant*magnetic*field*of*magnitude*& ' = 1.5 T is*applied*into*the*page.*suppose*that*you* move*the*rod*to*the*right*with*a*constant*velocity*+ = 2 m/s.*what*is*the*current*in*the*rod*in* Amperes*(Enter*a*number*without*the*unit)? & '! + 0 Rod INTRODUCTION 20
Induction)answer Conducting*parallel*rails*with*negligible*resistance*are*connected*by*a*resistor*with*a*resistance* of*! = 10Ω,*and*a*conducting*rod*of*length*& = 0.5 m is*free*to*slide*on*the*rails*as*shown.*an* external*uniform*constant*magnetic*field*of*magnitude** + = 1.5 T is*applied*into*the*page.* Suppose*that*you*move*the*rod*to*the*right*with*a*constant*velocity*- = 2 m/s.*what*is*the* current*in*the*rod*in*amperes*(enter*a*number*without*the*unit)? 1 = E 345 = 7 89: 6 6 = ;.< = >?/@ +.<? ;+ A = 0.15 A * + Follow%up:*Which*direction*does*the*current*flow*in*the*rod?! - & Rod INTRODUCTION 21