D d x d d ρ x ρ 1 x d d x ρ 1 x d x d 12 an

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d d x d (d) ρ x ( ) = ρ 0 1 + x / d ( ) d x 0 ρ 0 1 x / d ( ) 0 x d # $ % & %
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12) An infinitely long cylinder of radius R with uniform volume charge density ρ 0 has an off-axis hole of radius b with center a distance d away from the center of the cylinder. What is the electric field within the hole? Hint: Replace the hole by the superposition of volume charge distributions of density ρ 0 and - ρ 0 . Convert the cylindrical coordinates to Cartesian coordinates for ease of vector additions. 13) Find the potential difference between the following surface charge distributions: (a) Two parallel sheets of surface charge of opposite polarity ± σ 0 and spacing a. (b) Two coaxial cylinders of surface charge having infinite length and respective radii a and b . The total charge per unit length on the inner cylinder is λ 0 while the outer cylinder is - λ 0 . (c) Two concentric spheres of surface charge with respective radii R 1 and R 2 . The inner sphere carries a uniformly distribution surface charge with total charge q 0 . The outer sphere has total charge -q 0 .
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