303L-HW2 - erro(jmf2547 HW 02 berk(60290 This print-out...

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fierro (jmf2547) – HW 02 – berk – (60290) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points You have 2 . 6 kg of water. One mole of water has a mass of 18 . 1 g / mol and each molecule of water contains 10 electrons since water is H 2 O. What is the total electron charge contained in this volume of water? Correct answer: 1 . 38409 × 10 8 C. Explanation: Let : N A = 6 . 02214 × 10 23 molec / mol , q e = 1 . 6 × 10 - 19 C / electron , m = 2 . 6 kg , M = 18 . 1 g / mol = 0 . 0181 kg / mol , and Z = 10 electrons / molec . The mass is proportional to the number of molecules, so for m grams in n molecules and M grams in N A molecules, m M = n N A n = m M N A Since 10 electrons are in each molecule of water, then the total number of electrons n e in the coin is n e = Z n = Z m M N A and the total charge q for the n e electrons is q = n e q e = Z m N A q e M = (10 electrons / molec) 2 . 6 kg 0 . 0181 kg / mol × ( 6 . 02214 × 10 23 molec / mol ) × ( 1 . 6 × 10 - 19 C / electron ) = 1 . 38409 × 10 8 C . 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 Coulomb’s law? 1. Use R for the distance. 2. The result of the calculation is zero. cor- rect 3. Use 2 π R for the distance. 4. Use 2 R for the distance. 5. None of these. Explanation: By symmetry and using the fact that the charge is uniformly distributed along the cir- cumference, the total force on q is zero. For example, consider a small element of charge δQ on the circle. The force on q is along the vector connecting δQ and q . But on the ex- act opposite side there is another element of charge δQ 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 (part 1 of 2) 10.0 points Two conducting spheres have identical radii. Initially they have charges of opposite sign and unequal magnitudes with the magnitude of the positive charge larger than the mag- nitude of the negative charge. They attract each other with a force of 0 . 123 N when sepa- rated by 0 . 6 m. + + + + Initial The spheres are suddenly connected by a thin conducting wire, which is then removed. + + Connected
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fierro (jmf2547) – HW 02 – berk – (60290) 2 Now the spheres repel each other with a force of 0 . 03 N. + + Final What is the magnitude of the positive charge?
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