Two Physics 2 questions: 1) A solid plastic sphere of radius R1 = 8.00 cm is con

Question

Two Physics 2 questions:

1) A solid plastic sphere of radius R1 = 8.00 cm is concentric with an aluminum spherical shell with inner radius R2 = 14.0 cm and outer radius R3 = 17.0 cm (see figure below). Electric field measurements are made at two points: At a radial distance of 34.0 cm from the center, the electric field has magnitude 8.35 103 N/C and is directed radially outward, and at a radial distance of 12.0 cm from the center, the electric field has magnitude 2.00 104 N/C and is directed radially inward. What are the net charges on the following?

(a) the plastic sphere: ___________ C

(b) the aluminum spherical shell: ____________C

(c) What are the charges on the inner and outer surfaces of the aluminum spherical shell?

2) A cube with sides of 32.0 cm is placed in a nonuniform electric field

where x, y, and z are measured in meters and E is in N/C. Determine the electric flux through each of the six faces of the cube, assuming the cube has a corner at the origin and sides along the x, y, and z axes.

N · m2/C

_________ N · m2/C

Explanation / Answer

1. gIVEN
   inner plastic sphere, radius R1 = 0.08 m
   outer aluminium shell, inner radius, R2 = 0.14 m
   outer aluminium shell, outer radius, R3 = 0.17 m

   E(r) = 8.35*10^3 N/C at r = 0.34 m ( radially outwards)
   E(r) = -2*10^4 N/C at r = 0.12 m ( radially inwards)

   let charge on the shell be q, charge on sphere = Q
   then from gauss law
   at r = 12 cm
   E*4*pi*r^2 = Q/epsilon
   -2*10^4 = 8.98*10^9*Q/0.12^2
   a.    Q = -3.2071*10^-8 C

   at r= 0.34 m
   E*4*pi*r^2 = (q + Q)/epsilon
   8.35*10^3 = (q - 3.2071*10^-8)*8.98*10^9/0.34^2
   b.    q = 1.395*10^-7 C

   Now let inner surfaceof the shell have charge qin, outer surface qout
   then E(r) = 0 for r < R3 and r > R2
   hence qin = -Q = 3.2071*10^-8 C

   also, qout + qin = q
   qout = 1.07429*10^-7 C

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