You're going to find the electric field at a point P due to a line of charge. This line of charge isinfinitely long, although you can consider the charges within a length L which has a charge density ofλ. Let P be a distance "D" away from the line.If you get confused with any of the steps, see if you can compare with how we found the electric fielddue to a point charge using Gauss's law.1. Draw a suitable Gaussian surface on the picture below.ᎠP.L2. Add a little square (or other small area) on the Gaussian surface you drew, and draw the vectorperpendicular to it in order to represent a vector for dA somewhere on the gaussian surface. dA is theinfinitesimal area element on your drawing.3. Draw vectors for the electric field caused by L on the Gaussian surface.4. Write down an equation for the linear charge density 2.5. Write down Gauss's law, and use #4 to substitute on one side.6. Simplify the other side of Gauss's law based on the geometry of what you did in #2 and #3. Thereare two simplification steps you can do.7. Use an equation for the surface area of the shape you drew in #1 to eliminate the integral, then solvefor the electric field.

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