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- PHY102 Physics II © Dr.Cem Özdoğan
- 23-7 Applying Gauss’Law: Cylindrical Symmetry
- Figure 23-12 shows a section of an infinitely long cylindrical plastic rod with a uniform positive linear charge density .
- Let us find an expression for the magnitude of the electric field E at a distance r from the axis of the rod.
- Gaussian surface should match the symmetry of the problem, which is cylindrical.
- Choose a cylinder of radius r and length h, coaxial with the rod. Because the Gaussian surface must be closed, include two end caps as part of the surface.
- At every point on the cylindrical part of the Gaussian surface, E must have the same magnitude E and must be directed radially outward (for a positively charged rod).
- The flux of E through this cylindrical surface is
- Then, applying the Gauss’s law:
- Compare with the solution at Chapter 22!!