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For multiple-choice questions, circle the letter of the one best answer (unless more than one answer is asked for) Show your work on free-response questions. Be sure to use proper units and significant figures in your final answers. Organization and neatness count, too. Do NOT use red ink please reserve that color for grading.2. a. Optional (no points): On the diagram of two equal and opposite charges below, neatly draw electric field lines (roughly 8 to 16 lines per charge). Indicate direction on ALL field lines with arrowheads. b. Optional (no points): With a different color pen/pencil or with dashed lines, draw roughly 6 to 12 equipotential lines, spanning from very near the charges to near the edge of the page. Show the electric field lines and equipotentials for the entire area between and surrounding the charges, nearly to the edge of the page. Shape, symmetry, and relative spacing of the lines DO matter, but you do not need to calculate anything - a quaitative sketch is fine. Both charges have a magnitude of 12.0 nC, but have opposite signs (as shown) The separation between the two charges is 50.0 cm, exactly horizontal. Location P is located exactly halfway between the two charges. Location P2 is located 35.0 cm directly above the right-hand charge. .(1 pt.) What is the net electrie potential at location Pı? (Assume zero potential at r-) Briefly show your work or justify your answer, but you do NOT need to show a long calculation d.(3 pts.) Find the net electrie potential at location P2. (Watch your signs! Assume zero potential atr) Show your work.d.(3 pts.) Find the net electrie potential at location P2. (Watch your signs! Assume zero potential atro.) Show your work. e. (3 pts.) Determine the net electric field (magnitude & direction) at location Pi. Show your work. (Note: Your direction for E should agree with the E-field line direction in your diagram above. Does it?) f. (5 pts.) Determine the net electric field (magnitude & direction) at location P2. Show your work completely. (Note: Your direction for E should agree with the E-field line direction in your diagram above. Does it?)

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2. 035* +0S o 35 ½ = 308-Sa,-176.954 = 131.616 V (0,2)と 3456 NIC

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