Implementing Gauss's law on a cylinder. You're going to find the electric field at a point P due to a cylinder made of an insulating material. Again, we'll assume an infinitely long cylinder, although you can consider a section with finite length L, and radius R. Let P be a distance "D" away from the central axis of the cylinder, which has a charge density p. Make sure to keep D and R straight, in terms of which you are using where. The drawing can help. 1. Draw a suitable Gaussian surface on the picture below. P 2. Add vectors for då of the gaussian surface, (the infinitesimal area elements) on the drawing. 3. Draw vectors for the electric field caused by L on the Gaussian surface. 4. Write down an equation for p. Plug in to a geometrical equation so that it is in terms of given variables. 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. 7. Use an equation for the surface area of the shape you drew to eliminate the integral, then solve for the electric field.
Implementing Gauss's law on a cylinder. You're going to find the electric field at a point P due to a cylinder made of an insulating material. Again, we'll assume an infinitely long cylinder, although you can consider a section with finite length L, and radius R. Let P be a distance "D" away from the central axis of the cylinder, which has a charge density p. Make sure to keep D and R straight, in terms of which you are using where. The drawing can help. 1. Draw a suitable Gaussian surface on the picture below. P 2. Add vectors for då of the gaussian surface, (the infinitesimal area elements) on the drawing. 3. Draw vectors for the electric field caused by L on the Gaussian surface. 4. Write down an equation for p. Plug in to a geometrical equation so that it is in terms of given variables. 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. 7. Use an equation for the surface area of the shape you drew to eliminate the integral, then solve for the electric field.
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Transcribed Image Text:Implementing Gauss's law on a cylinder.
You're going to find the electric field at a point P due to a cylinder made of an insulating material.
Again, we'll assume an infinitely long cylinder, although you can consider a section with finite length
L, and radius R. Let P be a distance "D" away from the central axis of the cylinder, which has a charge
density p.
Make sure to keep D and R straight, in terms of which you are using where. The drawing can help.
1. Draw a suitable Gaussian surface on the picture below.
P
L
2. Add vectors for då of the gaussian surface, (the infinitesimal area elements) on the drawing.
3. Draw vectors for the electric field caused by L on the Gaussian surface.
4. Write down an equation for p. Plug in to a geometrical equation so that it is in terms of given
variables.
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.
7. Use an equation for the surface area of the shape you drew to eliminate the integral, then solve for
the electric field.
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for step one can you provide the drawing of how you would do it on the original picture and for your Gaussian surface did you choose a square ?
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