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PHY 206 Prof. Andrii Iurov HOMEWORK SET 3 Given on Monday, November 1st, 2021 Due: Wednesday, November 17th, 2021 at 10:00 p.m. Fall 2021 semester Problem 1. Three point charges are located at the corners of a square of side a as shown in Fig. 1 O M A Figure 1: Schematic graph for Problem 1. Please find the potential (a) at the fourth corner (point A). (b) at the center of the square (point O). (c) at the middle of the lower side (point M ). Problem 2. Two electrons are initially located at a distance Di = 0.1 m and are moving towards each each other with the equal initial speeds Vi = 1, 000 m/s. Calculate their speeds when they are at a distance D1 = 0.1 cm? What will be the minimal distance between these two electrons? Problem 3. Two point charges Q1 = 2.3 · 10−6 C and Q2 = −1.7 · 10−5 C are placed at points A and B separated by a distance X = 0.023 cm, as shown in Fig. 2. Point M is in the middle between A and B, and point P is located Y = 0.092 cm above B. P A M B Figure 2: Schematic graph for Problem 1. Determine (a) VM − VP – the potential difference between points M and P . ~M − E ~ P – the difference between the fields at points M and P (magnitude and direction). (b) E Problem 4. A parallel-plate capacitor with plate area A and plate separation d = 0.73 mm is connected to a 27 − V battery. (a) (b) (c) Figure 3: Schematic graph for Problem 5. (a) Determine the unknown area A if the capacitance of the capacitor is C = 2.5 · 10−8 F . (b) Find the charge on the capacitor, the electric field, the capacitance, and the energy stored in the capacitor. (c) With the capacitor still connected to the battery, a slab of plastic with dielectric strength K = 2.65 is placed between the plates of the capacitor, so that the gap is completely filled with the dielectric (see panel (b) of Fig. 3). What are the new values of charge, electric field, capacitance, and the energy stored in the capacitor? (d) Same as in part (c) but the dielectric occupies only half of the space between the plates (see panel (c) of Fig. 3).

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