PES 112      Spring 2003 General Physics II

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Solutions to the problem sets will be available on the day following the day they are due. They will be on Reserve at the Library and also available in the Science Learning Center (Science 145).

Solutions to some problems in the book can be found on the web at the text book web site.

Answers to odd numbered problems are in the back of the book. If your answer differs slightly it is probably because you rounded off by plugging numbers into the problem early. The best method is to keep everything as algebraic symbols until the very end of the problem and then plug in the values. This will help to eliminate rounding errors. I will post the answers to the even numbered problems after the problem set has been turned in.

Be sure and SHOW YOUR WORK on all assigned problems.

Problem Sets:

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Problem Set 1: Due Wednesday, January 29, 2003

Chapter 23

• Problem # 2 - GRADED
  • answers: a: F_el = 1.59x10^-9 N, b: F_grav= 1.29x10^-45N so electric force is 1.24x10³⁶ times larger, c: q/m = 8.61x10^-11 to have the forces equal.
• Problem # 8
  • answers: x = 0.634d from left end. Stable equilibrium if third bead has positive charge.
• Problem # 16
  • answers: a: E = -599 N/C i - 2700 N/c j , b: F = -3.00 i - 13.5 j µN
• Problem # 25 - GRADED
• Problem # 42
  • answers: a = -5.76x10¹³ i m/s², b: v = 2.84x10⁶ i m/s, c: t = 4.93x10^-8 s
• Problem # 55 - GRADED

Common problems on this problem set:

• carelessness
• not showing work
• mC = microCoulombs = 10^-6 Coulombs
• nC = nanoCoulombs = 10^-9 Coulombs
• qq = q² not 2q
• confusion on definitions of sine and cosine
• average = 6.05 / 9

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Problem Set 2: Due Wednesday, February 5, 2003

Chapter 24

• Problem # 5 - GRADED
• Problem # 16
  • part b is intended to be quite simple - the charge is still surrounded by a sphere but you are only looking at the flux through half of that sphere.
  • be sure and answer in words the question about radius too!
  • answers: a: flux = 1.36x10⁶ Nm²/C , b: flux = 6.78x10⁵ Nm²/C , c: No
• Problem # 21 - GRADED
• Problem # 27 - GRADED
• Problem # 38
  • answers: use Gauss's Law to find charge density = 1.15x10^-9 C/m²
• Problem # 41
• Problem # 56
  • answers: a: Q = -4.00 nC, b: Q' = 9.56 nC, c: Q₁ = 4.00 nC Q₂=5.56 nC

Common problems on this problem set:

•  trouble identifying angles correctly for dot products
• missing units on answers
• area of a cylindrical surface (not counting the ends) - 2(pi)rL (not pi r²L- which has the wrong units)
• 1/0 = infinity !!!!! so does 1/0²
• SHOW YOUR WORK (especially on odd problems where the answers are in the back of the book)
• Problems that ask about flux are MUCH easier that problems that ask for E. Often you can use Gauss's Law and skip right over the E and A and just consider the charge enclosed.
• average = 7.21 / 9

If you want more practice, take a look at problems 15, 29, 47, 55, and 59. The solutions to all of these problems are on the web at the text book web site.

Chapter 25 (problems from sections 1-5)

Notice the Note in the book that says to assume a reference level of potential of V=0 at r=infinity unless told otherwise in the problem.

• Problem # 9
• Problem # 16 - GRADED
  • answers: a) V₁= 1.44x10^-7 V, b) DELTA V = -7.19x10^-8V, c) V at 1 cm = -1.44x10^-7V, V at 2cm = 7.19x10⁸ V
• Problem # 17
• Problem # 22 - GRADED
  • answer: U_e= 8.95 J
• Problem # 33
• Problem # 38 - GRADED
  • answers: a) for r<R E=0, b) for r>R E = kQ/r²
• Problem # 42
  • answer: V = -1.51 MV

Common problems on this problem set:

• read the problem carefully: potential energy and potential are different things !
• If asked for a potential difference:
  • do not just calculate one potential
  • do not ADD potentials (difference => subtraction)
• The total potential energy required to assemble a collection of charges from infinity (equation 25.14) is quite different from the potential energy of interaction of one test charge interacting with an existing collection of charges (equation 25.12 multiplied by the test charge).
• problems taking derivatives of constants and powers of r
• average = 7.5 / 9

 If you want more practice, take a look at problems 9, 23, 37, and 49. The solutions to all of these problems are on the web at the text book web site.

Chapter 26 (problems from sections 1-5)

• Problem # 6 - GRADED
  • answers: C = 11.1 nF, Q = 26.6C (many people just calculated Q directly without C and I gave full credit)
• Problem # 17 - GRADED
• Problem # 18
  • a) C = 3.53 micro F, b) V1 = 6.35 V, V2 = 2.65 V , c) Q1 = Q2 = 31.8 micro C
• Problem # 29
  • if you had trouble on this one, my solutions in the library and SLC have lots of pictures!
• Problem # 32
  • a) U = 0.15 J, b) V = 268 V
• Problem # 45 - GRADED

Common problems on this problem set:

• unit conversion: 1 km² = 10⁶ m² (not 1000)
• read the problem carefully - #6 said to treat this like a parallel plate capacitor
• read the problem and do each part !!
• average = 7.61 / 9

If you want more practice, take a look at problems 7, 11, 21, 35 and 57. The solutions to all of these problems are on the web at the text book web site.

Chapter 27

• Problem # 6- GRADED
  • answer: I = q/T = q(omega)/2 pi ..... where omega is the angular frequency
• Problem # 7
• Problem # 14
  • answer: a) R = 3.75 kOhms, b) length = 536 meters
• Problem # 27 - GRADED
• Problem # 30 - GRADED
  • answer: R_n = 5.56 kOhms, R_C = 4.44 kOhms
• Problem # 43
• Problem # 59

Common problems on this problem set:

• on Number 6, some people tried to use the expression for current that involved drift velocity. This concept is only defined inside a solid and so does not apply here.
• SHOW YOUR WORK
• On Number 30, many of your solutions were IDENTICAL to the Solutions Manual. Could you do this problem if it appears on the Exam? I encourage you to get help and talk to others - but make sure that YOU know how to do the problem.
• average = 7.24 / 9

If you want more practice, take a look at problems 3, 15, 25, 39 and 57. The solutions to all of these problems are on the web at the text book web site.

Chapter 28

• Problem # 3
• Problem # 11
• Problem # 16
  • answer: two resistors are 470 Ohms and 220 Ohms
• Problem # 22
  • answers: a) current through R1 = 0.385 mA, current through R2 = 3.08 mA, current through R3 = 2.69 mA; b) potential difference from c to f is -69.2V with point c at the higher potential.
• Problem # 23 - GRADED
  • I fiind the solution manual confusing for this problem. My solutions on reserve in the library and SLC show a much more straight-forward solution.
• Problem # 34 - GRADED
  • answers: a) RC = 12.0 seconds; b) q(t) = 36 micro C (1 - e^-t/12) ... I(t) = 3 microA e^-t/12
• Problem # 53 - GRADED

Common problems on this problem set:

• SHOW YOUR WORK
• Some trouble setting up Kirchhoff's Rules - although most of you appear to be getting this OK.
• The maximum charge on a capactor = VC (or emf x C).
• When doing Kirchhoff's loop rule, the reason it all adds to zero is that you are back where you started and there is no potential difference. If you do NOT come back to where you started, then the 0 is replaced by the potential difference between where you started and where you stopped.
• In order for a current to flow, there must be a complete circuit. If the circuit is broken, no current will flow. In problem 53 no current will flow in the small wire with the 4V power supply or in the small wire with the 10 Ohm resistor.
• average = 5.23 / 9

If you want more practice, take a look at problems 1, 9, 19, 29, and 47. The solutions to all of these problems are on the web at the text book web site.

Chapter 29

• Problem # 4 - GRADED
  • answers: a) F = 8.67 x 10^-14N, b) a = 5.19 x 10¹³ m/s²
• Problem # 7 - GRADED
• Problem # 18
  • answers: segment ab F = 0, segment bc F = 0.4 N in -i direction, segment cd F = 0.4 in -k direction, segment da F= 0.4 in (k + i) direction
• Problem # 27 - GRADED
• Problem # 34
  • answer: B = 6.56 x 10^-2 Tesla

Common problems on this problem set:

• SHOW YOUR WORK
• UNITS !!
  • trouble converting units
  • kg is the MKS unit for mass (not grams)
• Remember that vectors have a direction as well as a magnitude
• average = 7.86/9

If you want more practice, take a look at problems 1, 13, 21, 25, and 47. The solutions to all of these problems are on the web at the text book web site.

Chapter 30 (sections 1-4)

• Problem # 2
  • answer: B = 2.61 x 10^-7 T into the page
• Problem # 7 - don't work too hard
• Problem # 18 - GRADED
  • answers: a) currents are in opposite direction, b) I = 67.8 Amps
• Problem # 21
• Problem # 24 - GRADED
  • answers: a) B = 1 x 10^-5 T, b) r = 2.50 cm beyond the conductor's surface
• Problem # 31 - need Ohm's Law, find n by inverting the wire width per turn - GRADED

Common problems on this problem set:

• SHOW YOUR WORK
• confusion over radius sometimes - when you see an "r" in an equation what is it the radius or distance of?
• average = 6.50/9

If you want more practice, take a look at problems 5, 19, 25, 29, and 55. The solutions to all of these problems are on the web at the text book web site.

Chapter 30 (section 8) and Chapter 31

• Chapter 30
  • Problem # 43 - GRADED
• Chapter 31
  • Problem # 4
    • answers: a) emf = (AB_max / tau) e^-t/tau , b) at t = 2 s emf = 3.79 mV, c) max at t=0 emf = 28 mV
  • Problem #14 - GRADED
    • answer: emf = -N(mu_o)nI_max (pi) R² (alpha) e^-(alpha)t
  • Problem # 23
  • Problem # 26
    • answers: a) current to the right in resistor, b) current to the right, c) current to the right d) B into the paper
  • Problem # 35 - GRADED

Common problems on this problem set:

• SHOW YOUR WORK
• some confusion on symbols (N vs n, r vs. R)
• some problems taking derivatives
• average = 7.3/9

If you want more practice, take a look at problems 5, 7, 37, 45, and 73. The solutions to all of these problems are on the web at the text book web site.

Chapter 32

• Problem # 8 - GRADED
  • answer: flux = 1.92 x 10^-5 T m²
• Problem # 9 - GRADED
• Problem # 19
• Problem # 34 - GRADED
  • answers: a) U = 27.8 J, b) t = 1.85 x 10^-2 s
• Problem # 44
  • answer M = 1.38 x 10^-7 H
• Problem # 49

Common problems on this problem set:

• SHOW YOUR WORK
• missing signs in places where it matters (like dI/dt on 32.9)
• average = 8.3/9

If you want more practice, take a look at problems 7, 21, 29, 35, and 55. The solutions to all of these problems are on the web at the text book web site.

Chapter 33

• Problem # 7
• Problem # 12 - GRADED
  • answer: (I_max = 22.5 A, I(t) = 19.5 A) U = 3.80 J
• Problem # 25
• Problem # 30
  • answer:(X_L - X_C) = 60.0 Ohms, PHI = 53.1 degrees, I_rms = 2.80 A, P = 353 W.

Chapter 34

• Problem # 4 - GRADED
  • answer = 38 pT
• Problem # 13 - GRADED
• Problem # 23

Common problems on this problem set:

• some trouble with the phase angle on 33.12. When you are told that the current is zero at t=0, that is telling you the phase angle.
• average = 8.07/9

If you want more practice, take a look at Chapter 33 problems 11, 23, 29, and 55 and Chapter 34 problems 5, 15, 17. and 29. The solutions to all of these problems are on the web at the text book web site.