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HW02-solutions

# HW02-solutions - Munoz(gm7794 HW02 TSOI(92515 1 001 10.0...

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Munoz (gm7794) – HW02 – TSOI – (92515) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The diagrams below depict three electric field patterns. Some of these patterns are physi- cally impossible. Assume these electric field patterns are due to static electric charges outside the regions shown. (a) (b) (c) Which electrostatic field patterns are phys- ically possible? 1. (b) and (c) 2. (a) and (c) 3. (a) and (b) 4. (a) only 5. (c) only 6. (b) only correct Explanation: Electrostatic lines of force do not intersect one another. Neither do they form a closed circuit (unless there is a changing magnetic field present). 002 10.0 points Given symmetrically placed rectangular insu- lators with uniformly charged distributions of equal magnitude as shown in the figure. x y + + + + + + + + + + + + - - - - - - In this figure, at the origin, the net field E net is 1. zero and the direction is undefined. 2. along 30 direction in the first quadrant. 3. aligned with the positive x -axis. 4. aligned with the negative y -axis. correct 5. along 225 direction in the first quad- rant. 6. aligned with the negative x -axis. 7. along 60 direction in the first quadrant. 8. along 135 direction in the first quad- rant. 9. aligned with the positive y -axis. 10. along 45 direction in the first quadrant. Explanation: At the origin the fields from the bottom slab points towards the negative y axis (towards the negatively charged slab). The field from the right and left slabs have equal magnitudes at the origin and are sym-

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Munoz (gm7794) – HW02 – TSOI – (92515) 2 metric about the y axis. The field from the right and left slabs point away from each pos- itively charged slab. Therefore the x compo- nent of the field cancels at the origin. The net field from the right and left slabs points towards the negative y axis (away from the positively charged slab). Hence, the sum of the electric fields from all three slabs is aligned with the negative y -axis. 003 (part 1 of 2) 10.0 points A dipole (electrically neutral) is placed in an external field. + (a) + (b) - + - + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + - + - + (c) (d) For which situation(s) shown above would the net force on the dipole be equal to zero? 1. ( b ) only 2. ( a ) and ( b ) 3. ( c ) only 4. ( a ) only 5. ( a ) and ( d ) 6. ( b ) and ( d ) 7. ( c ) and ( d ) correct 8. ( d ) only 9. ( b ) and ( c ) 10. ( a ) and ( c ) Explanation: The force on a charge in the electric field is given by F = q E and the torque is defined as T = r × F Δ E = k Δ q r 2 ˆ r E = Δ E i . Symmetry of the configuration will cause some component of the electric field to be zero. Gauss’ law states Φ S = E · dA = Q 0 . The electric dipole consists of two equal and opposite charges separated by a distance. In either situation ( c ) or ( d ), the electric field is uniform everywhere between the parallel infinite plates. Thus, the electric force on one charge is equal but opposite to that on another so that the net force on the whole dipole is zero. By contrast, electric fields are nonuniform for situations both ( a ) and ( b ).
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