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Final Review PHYS 212 Chapter 21 36.(II) Two point charges Q1=-25µC, and Q2=+45µC are separated by a distance of 12 cm. The electric field at the point P (see Fig. 21–58) is zero. How far from Q1 is P? Chapter 22 27. (II) Two thin concentric spherical shells of radii r1 and r2 r1 < r2 contain uniform surface charge densities and respectively (see Fig. 22–31). Determine the electric field for (a) 0 < r < r1 , (b) r1 < r < r2 , and (c) r > r2 . (d) Under what conditions will E 0 for r > r2 ? (e) r < r < r2 ? Under what conditions will E 0 for 1 Neglect the thickness of the shells. Chapter 22 34. (II) A very long solid non-conducting cylinder of radius R0 and length l0(R0≪ l0) possesses a uniform volume charge density 𝜌𝐸 (C/cm3), Fig. 22–34. Determine the electric field at points (a) outside the cylinder (R› R0) and (b) inside the cylinder (R‹ R0). Do only for points far from the ends and for which R≪ l. Chapter 24 30.(II) Suppose in Fig. 24–23 that C1=C2=C3=16µF and C4=28.5µF. If the charge on C2 is Q2=12.4µC, determine the charge on each of the other capacitors, the voltage across each capacitor, and the voltage Vab across the entire combination. Chapter 24 59. (II) Two different dielectrics each fill half the space between the plates of a parallel-plate capacitor as shown in Fig. 24–30. Determine a formula for the capacitance in terms of k1,k2 ,the area A of the plates, and the separation d. [Hint: Can you consider this capacitor as two capacitors in series or in parallel?] Chapter 24 62. (II) Two identical capacitors are connected in parallel and each acquires a charge Q0 when connected to a source of voltage V0 . The voltage source is disconnected and then a dielectric (K=3.2) is inserted to fill the space between the plates of one of the capacitors. Determine (a) the charge now on each capacitor, and (b) the voltage now across each capacitor. Chapter 26 25. (III) Consider the network of resistors shown in Fig. 26–43. Answer qualitatively: (a) What happens to the voltage across each resistor when the switch S is closed? (b) What happens to the current through each when the switch is closed? (c) What happens to the power output of the battery when the switch is closed? (d) Let R1=R2=R3=R4= 125Ω and V= 22.0V. Determine the current through each resistor before and after closing the switch. Are your qualitative predictions confirmed? Chapter 26 48.(II) The RC circuit of Fig. 26–59 (same as Fig. 26–18a) has R=8.7kΩ and C=3.0μF. The capacitor is at voltage V0 at t=0 s when the switch is closed. How long does it take the capacitor to discharge to 0.10% of its initial voltage? Chapter 27 19. (II) A doubly charged helium atom whose mass is 6.6 X 10-27 kg is accelerated by a voltage of 2700 V. (a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field? (b) What is its period of revolution? Chapter 27 25. (II) A proton moves through a region of space where there is a magnetic field B 0.45 ˆi 0.38 ˆj T and an electric field E 3.0 ˆi 4.2 ˆj 3 103 V/m. At a given instant, the proton’s velocity is v 6.0 ˆi 3.0 ˆj 5.0 kˆ 3 103 m/s. Determine the components of the total force on the proton. Chapter 28 21. (II) Two long wires are oriented so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. 28– 39). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 12.0 A? Chapter 28 35. (II) A circular conducting ring of radius R is connected to two exterior straight wires at two ends of a diameter (Fig. 28–44). The current I splits into unequal portions (as shown) while passing through the ring. What is at the center of the ring?