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Part B. Short questions. Steps and explanations are required. 1. [30 pts] Two charges q and Q are fixed in place along the x axis. Q = +3.8 nC is at x = -2.0 cm and unknown charge q is located at x = 2.0 cm. [Answer in 2 significant figures] a) [10 pts] It is found that the net electric field is zero at x = -0.76 cm. What is the magnitude and sign of charge q? b) [8 pts] Sketch both the equipotential lines and the electric field for the system (you need to have at least 5 field lines for the smallest charge and 6 potential lines for each charge) 5 c) [12 pts] A proton is fired at infinity towards q along the line of the two charges with speed 7.4×104 m/s. How close the proton from charge q before it turns around? 6 2. [30 pts] Three charges are located at three corners of a square as shown in the figure. [Answer in 3 significant figures] a) [12 pts] How much work is required to bring in a fourth charge (q 4=+4.0 μC) to the last corner of the square at constant speed? 7 b) [13 pt] What is the net electric field magnitude and direction at the center of the square due to the four charges? 8 c) [5 pts] Sketch the electric field for the system (you need to have at least 5 field lines for the smallest charge) 9