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You're going to find the electric field at a point P due to a line of charge. This line of charge is infinitely long, although you can consider the charges within a length L which has a charge density of 2. 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 field due to a point charge using Gauss's law.

You're going to find the electric field at a point P due to a line of charge. This line of charge is infinitely long, although you can consider the charges within a length L which has a charge density of 2. 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 field due to a point charge using Gauss's law.

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You're going to find the electric field at a point P due to a line of charge. This line of charge is infinitely long, although you can consider the charges within a length L which has a charge density of λ. 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 field due to a point charge using Gauss's law. 1. Draw a suitable Gaussian surface on the picture below. Ꭰ P. L 2. Add a little square (or other small area) on the Gaussian surface you drew, and draw the vector perpendicular to it in order to represent a vector for dA somewhere on the gaussian surface. dA is the infinitesimal 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. There are 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 solve for the electric field.
Transcribed Image Text:You're going to find the electric field at a point P due to a line of charge. This line of charge is infinitely long, although you can consider the charges within a length L which has a charge density of λ. 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 field due to a point charge using Gauss's law. 1. Draw a suitable Gaussian surface on the picture below. Ꭰ P. L 2. Add a little square (or other small area) on the Gaussian surface you drew, and draw the vector perpendicular to it in order to represent a vector for dA somewhere on the gaussian surface. dA is the infinitesimal 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. There are 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 solve for the electric field.
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