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Unformatted text preview: Solution Derivations for Capa #5 1) A positive charge of Q = 5 . 30 C is fixed in place. From a distance of r i = 4 . 40 cm a particle of mass m = 6 . 00 g and charge q = +3 . 70 C is fired with an initial speed of v = 60 . m/s directly toward the fixed charge. What is the minimum distance r f between the two charges? Q = Given r i = Given m = Given q = Given v = Given r f = ? This problem is easiest to solve with energy considerations. KE i + PE i = KE f + PE f 1 2 mv 2 + kqQ r i = 0 + kqQ r f mv 2 2 kqQ + 1 r i = 1 r f r f = 1 mv 2 2 kqQ + 1 r i 2) The electric potential along the x-axis (in kiloVolts ) is plotted versus the value of x , (in meters ). Evaluate the x-component of the electrical force on a charge of 4 . 50 C located on the x-axis at x = 0 . 4 m . q = Given Once again, you must hit this problem right on the money. Get out the laser timers and calculate the exact distance between the points. Well, you need to be pretty accurate anyway. Remember that the electric field is E =- dV dl and that force is F = qE. 3) Four charges are arranged at the corners of a square as shown in the figure. Q 1 is at (- L/ 2 ,L/ 2), Q 2 is at ( L/ 2 ,L/ 2), point a is at the origin and Q 1 = Q 2 =- Q 3 =- Q 4 . Which of the following statements correctly describe the electric field E and the true potential at points a, b, and c? Enter the letters of true statements in alphabetical order; e.g. ACF 1 QUESTION: A) The magnitude of the E field at b is greater than at c. B) The E field at b points towards a. C) The E field at c is perpendicular to the x axis. D) The potential at a is zero. E) a, b, and c each lie on a different equipotential surface. F) The potential at b is greater (more positive) than the potential at a. G) The E field at b is zero. ANSWER: A) True, b is closer to Q 2 and Q 4 than is c, so the electric field is strong. B) False, the electric field points straight down, toward the negative charges....
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