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1. What is the net electric flux through each of the four surfaces shown in the figure below? (Assume Q1 = 23.6 µC and Q2 = 47.2 µC.) ΦE,1 = N · m2/C ΦE,2 = N · m2/C ΦE,3 = N · m2/C ΦE,4 = N · m2/C 2. The colored regions in the figure below represent four three-dimensional Gaussian surfaces A through D. The regions may also contain three charged particles, with and that are nearby as shown. What is the electric flux through each of the four surfaces? Note: A charge is within a region if it is located inside the perimeter shown for that region. = N · m2/C = N · m2/C = N · m2/C = N · m2/C 3. A spherical shell of radius 1.60 m contains a single charged particle with at its center. (a) What is the total electric flux through the surface of the shell? N · m2/C (b) What is the total electric flux through any hemispherical portion of the shell's surface? N · m2/C q1 = +5.40 nC, q2 = −5.40 nC, q3 = +8.60 nC, ΦE, A ΦE, B ΦE, C ΦE, D q = 16.0 nC 4. The figure below shows a very long tube of inner radius a and outer radius b that has uniform volume charge density ρ. Find an expression for the electric field between the walls of the tube—that is, for a < r < b. (Use any variable or symbol stated above along with the following as necessary: ε0.) = r̂ E 5. The figure below shows a very long, thick rod with radius R, uniformly charged throughout. Find an expression for the electric field inside the rod (Use the following as necessary: r, R, λ for the linear charge density of the rod, and ε0.) = r̂ Use the equation, to check your solution at the surface, where (Use the following as necessary: R, λ, and ε0.) = r̂ (r < R). E E = r̂ 1 2πε0 λ r r = R. E(r = R) 6. Two uniform spherical charge distributions (see figure below) each have a total charge of 17.5 mC and radius Their center-to-center distance is 37.50 cm. Find the magnitude of the electric field at point B, 7.50 cm from the center of one sphere and 30.0 cm from the center of the other sphere. N/C R = 15.2 cm. 1. A very large, flat slab has uniform volume charge density ρ and thickness 2t. A side view of the cross section is shown in the figure below. (a) Find an expression for the magnitude of the electric field inside the slab at a distance x from the center. (Use any variable or symbol stated above along with the following as necessary: ε0.) (b) If and calculate the magnitude of the electric field at N/C E = ρ = 7.70 µC/m3 2t = 8.00 cm, x = 1.50 cm. PART 2 2. A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions M/L3. (Use the following as necessary:, A, r, R, and ε0.) (a) Calculate the total charge in the sphere. (b) Using the answer to part (a), write an expression for the magnitude of the electric field outside the sphere—that is, for some distance (c) Find an expression for the magnitude of the electric field inside the sphere at position ρ(r) = A/r, Q = r > R. E = r < R. E =

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