NAME: PHYSISCS 131 Fall21-Midterm#1-Chapters 22,23,24 Take Home Midterm #1 due Wednesday, September 22, before lecture time, no exceptions

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NAME: PHYSISCS 131 Fall21-Midterm#1-Chapters 22,23,24 Take Home Midterm #1 due Wednesday, September 22, before lecture time, no exceptions. Please submit a single PDF file for the midterm and a single PDF file. Please note the problems are worth different points. Budget your time accordingly. STRONG REMINDER: No google, sharing, or looking up any solutions. 1.(5 points) A +7.00 μC point charge and -9.00 μC point charge are placed along the x-axis at x = 0.000 cm and x = 40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not experience any net electric force due to the other two charges? 2.(10 Points) All the charges, in the figure below, are point charges and the charge in the middle is Q = -3.1 nC. For what charge q1 will charge q2 be in static equilibrium? 3.(10 Points) The figure shows two tiny 5.0-g spheres suspended from two very thin 1.0-m-long threads. The spheres repel each other after being charged to and hang at rest as shown. What is the angle θ? (k = 1/4πε0 = 8.99 × 109 N ? m2/C2) 4.(10 Points) At a distance of 4.3 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center? (ε0 = 8.85 × 10-12 C2/N ? m2) 5.(5 Points) In the figure, a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it. A point charge Q is placed at the center of the ring. The electric field is equal to zero at field point P, which is on the axis of the ring, and 0.73 m from its center. (ε0 = 8.85 × 10-12 C2/N ? m2) What is the value of the point charge Q ? 6.(10 Points) A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial velocity of vo = 1.0 × 107 m/s, as shown in the figure. (e = 1.60 × 10-19 C, ε0 = 8.85 × 10-12 C2/N ? m2, mel = 9.11 × 10-31 kg) What is the distance of closest approach of the electron to plate B? 7.(15 Points) The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is -40 nC/m and the linear charge density on the outer conductor is -50 nC/m. The inner and outer cylindrical surfaces are respectively denoted by A, B, C, and D, as shown. (ε0 = 8.85 × 10-12 C2/N ? m2) The magnitude of the electric field at a point that is 94 mm from the axis is closest to 8.(15Points) Two concentric spheres are shown in the figure. The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 µC. No other charges are present. The radii shown in the figure have the values R1 = 10.0 cm, R2 = 20.0 cm, and R3 = 30.0 cm. (k = 1/4πε0 = 8.99 × 109 N ? m2/C2) (a) Find the total excess charge on the inner and outer surfaces of the conducting sphere. (b) Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i) r = 9.5 cm, (ii) r = 15.0 cm, (iii) r = 27.0 cm, (iv) r = 35.0 cm. 9.(10 Points) A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries an excess charge of -500 nC. A point charge of +300 nC is present at the center. What is the surface charge density on the inner spherical surface? 10.- (10 Points) A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, as shown in the figure. The sphere carries a net excess charge of -500 nC. A point charge of +300 nC is present at the center. (k = 1/4πε0 = 8.99 × 109 N ? m2/C) What is the radial component of the electric field at a point that is 0.60 m from the center?