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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 23.5 Application: Infinite Line of Charge

Subsubsection Activities

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Activity 23.5.1. The Infinite Line of Charge.

Suppose you have an infinitely long wire with a uniform charge density \(\lambda\text{.}\) An imaginary cylindrical Gaussian surface with radius \(s\) and height \(h\) is centered on the wire. Point P is on the right edge of the Gaussian cylinder.
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A long, straight vertical wire with charge density lambda and a coaxial Gaussian cylinder with height h, radius s, and point P at its right edge.
Figure 23.5.1. An infinite wire and a cylindrical Gaussian surface.
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(a)

What direction do you expect the electric field to be at point P? How does the direction change as you move around the cylinder?
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(b)

Is the flux through the top endcap positive, negative, or zero? What about the bottom endcap?
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(c)

Is the flux through the outside surface of the cylinder positive, negative, or zero?
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(d)

Use Gauss’s Law to solve for the electric field at point P.
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  1. Find the charge enclosed in the surface.
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  2. Calculate the flux through each of the three surfaces.
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  3. Use this to find the net flux.
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  4. Use Gauss’s Law to solve for the magnitude of the electric field!
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(e)

Why would Gauss’s Law be a poor choice if you wanted to solve for the electric field due to a wire with finite length \(L\text{?}\)
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