5.2. Consider the vector A = ap Ao p. (a) Determine the surface flux of this...

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5.2. Consider the vector A = ap Ao p. (a) Determine the surface flux of this vector field through the surface of a cylinder centered at the origin with radius a, extending from z = -L/2 to +L/2. (b) Determine the volume integral of V A(r) over this same region. (c) Is the Divergence Theorem satisfied? 5.3. A uniform infinitely-wide sheet of surface charge density ps lies in the x-y plane at z = 0. Use Gauss' Law to determine the electric field E for z> 0 and z <0. What is the discontinuity of E at z=0? (b) Now replace the thin sheet of charge with a thick sheet of charge, of uniform charge density pv, filling the region from z = -a to z = +a. Use Gauss' Law to find the electric field E. Express your answer separately for the four regions z < -a, -a 5.2. Consider the vector A = ap Ao p. (a) Determine the surface flux of this vector field through the surface of a cylinder centered at the origin with radius a, extending from z = -L/2 to +L/2. (b) Determine the volume integral of V A(r) over this same region. (c) Is the Divergence Theorem satisfied? 5.3. A uniform infinitely-wide sheet of surface charge density ps lies in the x-y plane at z = 0. Use Gauss' Law to determine the electric field E for z> 0 and z <0. What is the discontinuity of E at z=0? (b) Now replace the thin sheet of charge with a thick sheet of charge, of uniform charge density pv, filling the region from z = -a to z = +a. Use Gauss' Law to find the electric field E. Express your answer separately for the four regions z < -a, -a