A very long solid cylinder with a radius R is uniformly charged. The charge density (charge per unit volume) is ρ (ρ >0)

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A very long solid cylinder with a radius R is uniformly charged.
The charge density (charge per unit volume) is ρ (ρ >0). Figure
A below depicts its cross-section.
Determine the electric field at point P. The distance from the
center of the rod to point P is 2R/3.
If the rod has a concentric cylindrical hole along the rod, with
a radius R/2, as shown in figure B, determine the electric field at
point P(2R/3, 0).
If the hole is shifted to the right by R/2, as shown in figure
C, determine the electric field at point P(2R/3, 0). Now the center
of the hole is at (R/2, 0).
If the cylindrical hole inside the rod has a radius of w and the
center of the hole is located at (a, b), as shown in figure D, find
the electric field at an arbitrary point (x, y) inside the hole.
Note that the hole is still parallel to the rod.

1 (31.49 KiB) Viewed 18 times

2 (12.55 KiB) Viewed 18 times

R 0 Figure A O X Ⓡ Figure B X R Figure C X
R O Figure D P. x