PHY303K.oldq1 - Shie Gary Oldquiz 1 Due 1:00 pm Inst Turner...

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Shie, Gary – Oldquiz 1 – Due: Sep 13 2004, 1:00 pm – Inst: Turner 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A circular ring made of an insulating mate- rial is cut in half. One half is given a charge - q uniformly distributed along its arc. The other half is given a charge + q also uniformly distributed along its arc. The two halves are then rejoined with insulation at the junctions J , as shown. x y - q + q J J - - - - - - - - - - - - - - - - - - + + + + + + + + ++ + + + + + + + + q e If there is no change in the charge distri- butions, what is the direction of the net elec- trostatic force on an electron located at the center of the circle? 1. toward the top of the page 2. to the right 3. into the page 4. toward the bottom of the page correct 5. to the left Explanation: Pay attention to the symmetry in the con- figuration. The whole system is symmetrical about the diameter perpendicular to the line connecting two junctions. Also, we know the electrostatic force is along the direction connecting the two charges; repulsive if two charges are of the same sign and attractive if two charges are of the opposite sign. There- fore, the force on the electron is parallel to the symmetrical axis and points to the pos- itive charge, i.e. toward the bottom of the page. 002 (part 1 of 1) 10 points From the electric field vector at a point, one can determine which of the following? I. The direction of the electrostatic force on a test charge of known sign at that point II. The magnitude of the electrostatic force exerted per unit charge on a test charge at that point III. The electrostatic charge at that point 1. III only 2. I, II and III 3. I only 4. I and II only correct 5. II and III only Explanation: The definition of the electrostatic force is ~ E = ~ F q . In another way, ~ F = q ~ E. This means ~ F is in the same direction of, or opposite di- rection to ~ E , depending on the sign of the charge. And if we only consider the magni- tude, F = qE , for a unit charge, the force on it is just F q = E . This is statement II. 003 (part 1 of 2) 10 points Consider a square with side a . Four charges + q , + q , - q , and + q are placed at the corners A , B , C , and D , respectively. + + - + D A C B a The magnitude of the electric field at D due
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Shie, Gary – Oldquiz 1 – Due: Sep 13 2004, 1:00 pm – Inst: Turner 2 to the charges at A , B , and C is given by 1. k ~ E k = 7 2 k q a 2 2. k ~ E k = 2 k q a 2 3. k ~ E k = 3 2 k q a 2 correct 4. k ~ E k = 3 k q a 2 5. k ~ E k = 5 2 k q a 2 6. k ~ E k = 2 k q a 2 7. k ~ E k = 9 4 k q a 2 8. k ~ E k = k q a 2 Explanation: The magnitudes of the electric fields at D due to A and C are E A = E C = k q a 2 since they are at a distance a , whereas E B = k q ( a 2) 2 = k q 2 a 2 since B is at a distance 2 a . 292 . 53 E C E A E B E A + E C E A + E B + E C + D As for directions, ~ E A (downwards since A is positive) and ~ E C (right since C is negative) are at right angles and can be added with Pythagoras theorem: k ~ E A + ~ E C k = k q a 2 1 + 1 = 2 k q a 2 This resultant vector points 45 down to the right. The vector ~ E B points at 135
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