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PHY 206 Prof. Andrii Iurov HOMEWORK SET 2 Given on Monday, October 04th, 2021 Due: Monday, October 25th, 2021 Fall 2021 semester Problem 1. A slight modification of Problem 5 (page 471) from our textbook. Two point charges Q1 = −6.7 µC and an unknown positive charge Q2 are placed between two oppositely charged plates, as shown in Fig. 1. The distance between the two charges is x = 13.5 cm. The electric field produced by the charged plates is uniform and equal to E = 25, 800 N/C. + + + + + A + + + + + + S + P B – Figure 1: Schematic graph for Problem 1. (a) Find the unknown charge Q2 if the net force acting on charge Q1 = −6.7 µC is directed towards Q2 and equal to F1,net = 0.00026 N . (b) Find the net force (both its magnitude and direction) acting on charge Q2 . (b) Find the electric field (both its magnitude and direction) at points P and S shown in Fig. 1. Assume that the vertical displacement y = AS = 4.5 cm. Problem 2. A slight modification of Problem 3 (page 472) from our textbook. An particle with a negative charge q = 5.8 · 10−7 and mass m = 3.1 · 10−4 enters a uniform electric field between two oppositely charged plates at an angle θ0 = 300 to the horizontal, as shown in Fig. 2. The path is symmetrical, so the particle leaves at the same angle θ0 . The uniform electric field created by the plates is Ec = 5, 000 N/C. The maximum vertical displacement of the charged particle particle is Y = 60.5 cm. + + + + + + + + + + + + – Figure 2: Schematic graph for Problem 2. (a) What is the length X of each charged plate? (b) What are the initial Vi and final Vf speeds of the particle? What is its speed Vm right in the middle of the plates? Hint. Please remember to include a downward gravity force mg (g = 9.8 m/s2 ) acting on the particle. Problem 3. ~ anywhere in space as a function of distance r from the center of each sphere Find the electric field E O for (a) (b) (c) Figure 3: Schematic graph for Problem 3. (a) A single spherical shell of radius R with charge density σ (per unit area). (b) two concentric spherical shells of radii 2R/3 and R each with charge density σ (per unit area). (c) A single spherical shell of radius R with charge density σ and a point charge q located at the center of the sphere. Problem 4. Two metallic spheres of radii R1 = 5 cm and R2 = 12.7 cm and charges q1 = 10.0 µC and q2 = −5.8 µC, correspondingly, are kept far away from each other. The spheres are connected by a thin conducting wire. What charge will flow through this wire after its ends are attached to the spheres?

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