(xw788) WANG homework 02 Turner (59070) This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. 001 10.0 points Four point charges, each of magnitude 14.96 C, are placed at the corners of a square 31.8 cm on a side. The value of Coulombs constant is 8.98755 109 N m2 /C2 . If three of the charges are positive and one is negative, nd the magnitude of the force experienced by the negative charge. Correct answer: 38.0751 N. Explanation: Let : ke = 8.98755 109 N m2 /C2 , d = 31.8 cm = 0.318 m , and Q = 14.96 C = 1.496 105 C . 1 + F14 + 3 The forces are F34 = F24 = ke F34 2 + = = 1 +2 2 1 +2 2 F34 (19.8907 N)
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= 38.0751 N . 002 10.0 points A charge Q is spread uniformly along the circumference of a circle of radius R. A point charge q is placed at the center of this circle. What is the total force exerted on q as calculated by Coulombs law? 1. Use R for the distance. 2. Use 2 R for the distance. 3. The result of the calculation is zero. correct 4. None of these. 5. Use 2 R for the distance. Explanation: By symmetry and using the fact that the charge is uniformly distributed along the circumference, the total force on q is zero. For example, consider a small element of charge Q on the circle. The force on q is along the vector connecting Q and q . But on the exact opposite side there is another element of charge Q which exerts an equal but opposite force on q . This is true for every point on the circle, so the net force is zero. 003 10.0 points A charge q1 of 4.00 109 C and a charge q2 of 2.10 109 C are separated by a distance of 39.0 cm. Find the equilibrium position for a third charge of +17.0 109 C by identifying its distance from q1 . Correct answer: 22.6143 cm. Explanation: Let : q1 = 4.00 109 C ,
F24 4
Q2 d2 = 8.98755 109 N m2 /C2 (0.318 m)2 = 19.8907 N 1.496 105 C
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ke Q 2 1 1 ke Q 2 F14 = = F34 = 2 2 d2 2 2d The vector sum of F24 and F34 is in the same direction as F14 , so F = F14 + F34 2 + F24 2 1 = F34 + 2 F34 2 2
WANG (xw788) homework 02 Turner (59070) q2 = 2.10 109 C , r1,2 = 39.0 cm , and q3 = 17.0 109 C . Equilibrium is possible only if q3 is between q1 and q2 , so r2,3 = r1,2 r1,3 . q1 q2 r2 The net electric force on q3 is zero, so Felectric = kC F1,3 q1 q3 2 r1,3 q1 2 r1,3 q1 2 r1,3 = F2,3 q2 q3 = kC 2 r2,3 q2 =2 r2,3 q2 = (r1,2 r1,3 )2
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Let : q = 35 C and qe = 1.60218 1019 C . The charge is proportional to the number of electrons, so q = n |qe | q 35 C n= = |qe | |1.60218 1019 C| = 2.18453 1020 .
kC
(r1,2 r1,3 )2 q2 = 2 q1 r1,3 r1,2 r1,3 = r1,3
005 (part 2 of 2) 10.0 points If each water molecule donates one electron, how much water is ionized in the lightning? One mole of water has a mass of 18.2 g/mol. Correct answer: 0.00660204 g. Explanation:
q2 q1 q2 q1 = r1,2
Let :
r1,2 r1,3 = r1,3 r1,3 1 + Thus r1,3 = r1,2 1+ = 1+ q2 q1 39 cm q2 q1
M = 18.2 g/mol and Na = 6.02214 1023 /mol .
Mass is proportional to the number of atoms in a substance, so for m grams in N atoms in the water and M grams in Na atoms in one mole, we have m N = M Na m N= Na M Since every water molecule donates one electron to the discharge, the total number of transferred electrons ne equals the total number nH2 O of ionized water molecules, so the total mass of the water ionized by the lightning bolt is ne M H 2 O NA 20 (18.2 g/mol) 2.18453 10 = 6.02214 1023 /mol = 0.00660204 g .
= 22.6143 cm from q1 .
2.1 109 C 4 109 C
004 (part 1 of 2) 10.0 points A strong lightning bolt transfers an electric charge of about 35 C to Earth (or vice versa). How many electrons are transferred? Avogadros number is 6.02214 1023 /mol. Correct answer: 2.18453 1020 . Explanation:
Mtotal = nH2 O mH2 O =
WANG (xw788) homework 02 Turner (59070) 006 10.0 points A negatively charged balloon has 2.4 C of charge. How many excess electrons are on this balloon? Correct answer: 1.5 1013 electrons. Explanation:
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What is its charge after 14000 electrons have been removed from it? Correct answer: 2.24 109 C. Explanation:
Let :
n = 14000 and qe = 1.6 1019 C .
Let : q = 2.4 C and = 1.60 1019 C/electron . The charge density is q N q N= = = 1.6 1019 2.4 106 C C/electron
The removal of n electrons leaves a positive charge on the balloon of q = n qe = (14000)(1.6 1019 C) 1 106 C 1C = 2.24 109 C . 009 10.0 points Two metal spheres that are initially uncharged are mounted on insulating stands, as shown.
= 1.5 1013 electrons . 007 10.0 points the Calculate net charge on a substance consisting of a combination of 3.9 1013 protons and 6.3 1013 electrons. Correct answer: 3.84 106 C. Explanation: Let:
X
Y
Np = 3.9 1013 charges , Ne = 6.3 1013 charges qe = 1.60 1019 C . Qnet = Np qp + Ne qe Qnet = (3.9 1013 )(1.6 1019 C) + (6.3 1013 )(1.6 1019 C) = 3.84 10
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qp = 1.60 1019 C ,
and
A negatively charged rubber rod is brought close to but does not make contact with sphere X. Sphere Y is then brought close to X on the side opposite to the rubber rod. Y is allowed to touch X and then is removed some distance away. The rubber rod is then moved far away from X and Y. What are the nal charges on the spheres? Sphere X 1. Negative 2. Positive 3. Positive 4. Negative 5. Zero Sphere Y Positive Negative correct Positive Negative Zero
C
008 10.0 points You have a neutral balloon. The charge of an electron is 1.6 1019 C.
WANG (xw788) homework 02 Turner (59070) Explanation: The force is repulsive if the charges are of the same sign, so when the negatively charged rod moves close to the sphere X, the negatively charged electrons will be pushed to sphere Y. If X and Y are separated before the rod moves away, those charges will remain on X and Y. Therefore, X is positively charged and Y is negatively charged. 010 10.0 points 1) Two uncharged metal balls, X and Y, stand on glass rods and are touching. X Y correct 4. Balls Y and X are both positive. 5. Balls Y and X are both negative.
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Explanation: Basic Concept: Electric induction caused by nearby charges. Solution: When a negative ball is moved near a metallic object (Y and X), the negative charge will attract positive charges, causing Y to have excess negative charge and X to have excess positive charge (Y and X are in contact, so the total net charge on Y and X should be zero). +
2) A third ball, carrying a negative charge, is brought near the rst two. X Y
Later, Y and X are separated, retaining their charges, so when the third ball is nally removed, Y will have net negative charge and X will have net positive charge. 011 10.0 points Two uncharged metal balls, X and Z, stand on insulating glass rods. A third ball, carrying a negative charge, is brought near the ball Z as shown in the gure. A conducting wire is then run between X and Z and then removed. Finally the third ball is removed. conducting wire Z X
3) Then the rst two balls are separated from each other, X Y
4) and the third ball is nally removed. X Y
When this is all four steps are done, it is found out that 1. Balls Y and X are still uncharged. 2. Ball Y is positive and ball X is negative. 3. Ball Y is negative and ball X is positive.
When all this is nished 1. balls X and Z are both positive, but ball X carries more charge than ball Z. 2. balls X and Z are both negative. 3. balls X and Z are both positive, but ball
WANG (xw788) homework 02 Turner (59070) Z carries more charge than ball X. 4. ball X is neutral and ball Z is negative. 5. ball X is neutral and ball Z is positive. 6. balls X and Z are still uncharged. 7. ball X is negative and ball Z is positive. correct 8. ball X is negative and ball Z is neutral. 9. ball X is positive and ball Z is negative. 10. ball X is positive and ball Z is neutral. Explanation: When the conducting wire is run between X and Z, some negative charge ows from Z to X under the inuence of the negative charge of the third ball. Therefore, after the wire is removed, X is charged negative and Z is charged positive. 012 10.0 points When combing your hair, you scu electrons from your hair onto the comb. Is your hair then positively or negatively charged? What about the comb? 1. Both are negatively charged. 2. Neither is charged. 3. Both are positively charged. 4. negatively charged; positively charged 5. positively charged; negatively charged correct Explanation: Excess electrons rubbed from your hair leave it positively charged. Excess electrons on the comb give it a negative charge. 013 10.0 points When one material is rubbed against another, electrons jump readily from one to the other. Why dont protons do that?
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1. Electrons are easily dislodged from the outer regions of atoms, but protons are held tightly within the nucleus. correct 2. Electrons travel at the speed of light while protons move very slowly. 3. Electrons are much lighter than protons. 4. Electrons can attract each other while protons repel each other. 5. Electrons are much heavier than protons. Explanation: Protons are held tightly within the nucleus.