Step 3: Construct the gaussian surface

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[line of charge]

A cylindrical tube is chosen to match the symmetry of the line of charge, centered about it, with a radius equal to the distance between the point of evaluation and the line of charge. The electric field anywhere on this surface has the same direction as the infinitesimal area vector and has a constant value everywhere on the surface. This surface is denoted by 2.

Since a gaussian surface must be closed, the tube is then capped with flat endcaps, 1 and 3. The electric field does not have the same value at all points on the endcaps, but the field vector is perpendicular to the area vector so there is no flux through the endcaps.

Last updated Sept. 25, 1997.
Copyright George Watson, Univ. of Delaware, 1997.