SCORE: ________ / 60 = ___________ Name_____________________________________ Alpha ____________
USNAPhysicsDepartment
LCDRShivok’sSP212
2016ThirdExamPRACTICEVERSION
Chapters2830(withinfinitesimalreview)
MagneticFields,MagneticForceandTorque,MagneticDipole‐moment,Capacitance,
Capacitorcharging,Biot‐SavartLaw,MagneticFieldduetoanArc,Ampere’sLaw,
Soleniods/Torids,InductorsandInductance,Faraday’sLaw,Lenz’sLaw,RLCircuits,
EnergyStoredinMagneticField,andMutualInductance.
Ifyouusetheseproblemstohelpyoudeterminetheareasinwhichyouare
weak,IbelievetheywillhelpyoupreparefortheThirdExamination.DONOT
confineyourstudytojusttheseproblems.ThisisaREVIEWPROBLEM
exercise,NOTanallencompassinggouge!
Exam III Breakdown Chapter 28 Chapter 29 Chapter 30 Review TOTAL Take‐Home In‐Class Questions Points Questions Points 4 11 3 18 3 8 2 12 5 13 3 18 3 8 2 12 15 40 10 60 1 Chapter 28 (18 points) 1. (6 points) Electrons with speed v enter a 2‐dimensional square chamber of side length d at point a. The electrons exit the chamber from the opposite corner (point b). There is a constant, uniform magnetic field in the chamber. Note that the path of the electrons is part of a circle. a. (2 points) What are the magnitude and direction of the magnetic field in the chamber? Your answer should be in terms of me (the mass of an electron), e (the elementary charge), v, and d. Show all steps. b. (1 point) How does the kinetic energy of the electrons at point b compare to that at point a? Is greater than it was, less than it was, or the same? Explain c. (3 points) Now we wish to send protons also with speed v through the chamber. They also enter at point a and must exit at point b. What changes must be made to the magnetic field? Explain and be specific. 2 2. (3 points) A particle with a charge of q = ‐ 2.0 C moves through a uniform magnetic field. 

Its velocity is v  (2iˆ  3 ˆj  1kˆ) m/s and its B field is B  (4.0iˆ  20 ˆj  12kˆ) Tesla. What is the Electric Field vector necessary to cause there to be no net force on this particle, in unit vector notation (including units)? Show all work: I J K = 3 
3. (2 points) A magnetic dipole has the dipole moment   (2iˆ  3 ˆj  4kˆ ) x10 4 A  m 2 is located in 
a magnetic field given by B  ( 1iˆ  4 ˆj ) x10 6 T . What is the potential energy associated with 

the arrangement? What is the angle  between  and B ? Show all work: 4. (2 points) A proton moves between the poles of a permanent magnet as shown. When
the proton’s velocity is directed toward the bottom of the page, the magnetic force
on the proton is directed: A)
B)
C)
D)
E)
out of the page
into the page
toward the top of the page
toward the left side of the page
toward the right side of the page Explain: 4 5. (2 points) A square loop carrying a counterclockwise current is in the plane of the paper.
The loop is in a uniform magnetic field directed into the paper. The following statement
is true. Explain: 6. (3 points) A circular loop of radius 3m carries a clockwise current of 3A. A circular loop in the same plane that has the same center has a radius of 2m and carries a counterclockwise current of 2A. What is the magnetic field at the center of the loops ? Show all work: 5 Chapter 29 (12 points) 7. (2 points) Figure below shows two parallel wires that carry currents i1 = 2.00 A and i2 = 3.00 A in opposite directions. They each have length L = 15.0 cm and they are separated by distance r = 2.00 cm. What is the force on wire 2 due to wire 1? Show all work: 6 8. (3 points) Figure below shows a wire (in cross section) that carries a current of 3.00 mA directly out of the plane of the figure toward you. What are the magnitude and direction of the magnetic field at point P, at radius r = 2.00 cm from the center of the wire? Show all work: 9. (3 points) Parallel wires carry equal and opposite currents as shown. The currents are 9.0 A each. One of the wires has a length of 0.15 m and the other wire is very long. If the separation of the wires is 0.0015 m, the force on the 0.15 m long wire is closest to A) 2.9x10-3 N to the left.
B) 2.9x10-3 N to the right.
C) 1.6x10-3 N to the right.
D) 1.6x10-3 N to the left.
E) 4.2x10-3 N to the left. Show all work: 7 10. (4points)Twoinfinitelylong,parallel,current‐carryingwireswithcurrents
directedoutofthepageareshown.Thewiresareperpendiculartotheplaneofthe
pageandareseparatedbyadistanceof0.80m.
Whatisthemagneticfieldvectoratapointmidwaybetweenthewires?
Whatistheforceperunitlengthofwire1duetowire2?
8 Chapter 30 (18 points) 11. (3 points) Figure below shows an RL circuit containing resistance R = 200Ω, inductance L = 800 μH, and an ideal battery with a potential difference of V = 12 V. When the switch is closed at time t = 0, current begins to appear in the circuit. What is the final (equilibrium) current (when changes have stopped)? At what time is the current i = 30 mA? Show all work: 12. (2 points) Figure below shows a circuit containing a battery, resistor 1, resistor 2 (R2 = 400Ω), and an inductor (L = 30.0 μH). Switch S has been closed a long time (so that equilibrium has been reached) and the current through the inductor is 20.0 mA. At time t = 0, the switch is opened. At what time t is the current through the inductor 10.0 mA (on its way down to zero)? A) .400 ms
B) 400 μs
C) 4.0 ms
D) 4.0 μs
E) None of the above
Show all work: 9 13. (3 points) Figure below shows a conducting loop as it is being pulled by a constant force from a region of uniform magnetic field. Assume that the field cuts off sharply along the vertical dashed line (this is, of course, very unrealistic but useful if were going to avoid spending several days working on this problem). The speed of the loop is a constant v = 2.00 mm/s. The loop height is L= 3.00 cm, and the loop resistance is 5.00 × 10‐5 Ω. The magnetic field has magnitude B = 6.00 × 10‐4 T and is out of the plane of the figure. What is the magnitude of the force F pulling on the loop? Show all work
10 14. (3 points) Figure below shows two circuits in which a conducting bar is slid at the same speed v through the same uniform magnetic field and along a U‐shaped wire. The parallel lengths of the wire are separated by 2L in circuit 1 and by L in circuit 2. The current induced in circuit 1 is counterclockwise. (a) Is the magnetic field into or out of the page? (b) Is the current induced in circuit 2 clockwise or counterclockwise? (c) Is the emf induced in circuit 1 larger than, smaller than, or the same as that in circuit 2? 11 15. (7 points total) Given a stiff wire bent into a rectangle (w = 10cm, l = 20cm) and
rotated at a constant angular speed of 960rev/min in a uniform magnetic field
B = 40mT. The magnetic field direction is indicated on the diagram.
a) (2 points) What is the frequency ( f ) of the induced emf? (watch those units!)
Show all work: b) (3 points) Starting with Faraday’s Law, determine what the amplitude of the
induced emf (E ) is?
Show all work: c) (3 points) Now assume the wire loop is stationary (with the orientation shown above). If the magnitude of the magnetic field changes with time according to B = 7t2 +12t, determine the magnitude of the induced emf (E ) at t = 2.5s after the field begins to change. What is the direction of the resultant current (clockwise or counterclockwise)? Explain how you determined that direction. 12 REVIEW (12 points) 16. (3 points) Figure below shows a simple circuit of a parallel‐plate capacitor of plate area A = 6.40 × 10‐5 m2 and plate separation d = 0.300 mm. The battery has a potential difference of V = 12.0 V. We disconnect the battery and then move a slab of porcelain (dielectric constant κ = 6.50) into the capacitor's gap, filling it. What are the following initially and after the porcelain is in place: plate charge, plate potential difference, capacitance, and electric field magnitude between the plates? Show all work:
13 17. (3 points) What is the magnitude of the electric field at the indicated point on the y‐axis due to the two charges lying on the x‐axis?  1

Q
sin( ) A. 2 
2
2 
 4 0 (a  b ) 
 1 Q 
B. 2 
2 
 4 0 (a ) 
 1

Q
C. 2 
2
2 

4
(
a
b
)

0


 1

Q
cos( ) D. 2 
2
2 
 4 0 (a  b ) 
 1 Q 
E. 2 
2 
 4 0 (b ) 
Show all work: 14 18. (3 points) Consider the RC circuit shown below. The switch has been in position 1 for a long
time. At t = 0 the switch is moved to position 2. At t = 4.0 s, the magnitude of the current in
the resistor is closest to
Show all work: 15 19. (3 points)
a. Find the magnitude and true direction of all currents in the following circuit.
Show all work: a. What is the voltage at point A if point F is grounded?
Show all work: 16 Check all your work with answers posted on my website and see me if you need help!
Make sure you showed all your work for all problems! Do the idiot check on your math…
Does 50 – 30 = 20 or did you fat finger the calculator?
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