How does a 'open surface' of a closed loop look like?

In summary, an open surface of a closed loop is a surface that is enclosed by a closed loop, but has at least one opening. This is different from a closed surface, which is completely sealed off by the loop. An example of an open surface of a closed loop is a donut shape. Understanding these surfaces is important in various fields and they can be visualized through mathematical equations, computer-generated images, or physical models.
  • #1
serverxeon
101
0
im on the topic of electricity and magnetism, and came across walter lewin's lecture.

i cannot visualise how the 'open surface' of this solenoid will look like

b7f9ye.png


is the open surface a riemann surface? or something else?

[PLAIN]http://wiki-images.enotes.com/thumb/b/b5/Riemann_sqrt.jpg/180px-Riemann_sqrt.jpg

thanks
 
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  • #2
I believe the correct terminology is helicoid.

A Riemann surface is something else entirely. I'm not a mathematician, but as I understand it, a Riemann surface is just a way to visualize different branches of a function and how they are related to each other.
 

1. What is an open surface of a closed loop?

An open surface of a closed loop is a surface that is enclosed by a closed loop, but has at least one point that is not part of the loop. This means that the surface is not completely sealed off by the loop and has at least one opening.

2. How is an open surface of a closed loop different from a closed surface?

A closed surface is completely enclosed by a closed loop and has no openings, while an open surface of a closed loop has at least one opening. This means that a closed surface is a complete, continuous surface, while an open surface of a closed loop is not.

3. Can you give an example of an open surface of a closed loop?

One example of an open surface of a closed loop is a donut shape, also known as a torus. The surface of the donut is enclosed by the loop, but has an opening in the middle.

4. What is the significance of understanding open surfaces of closed loops?

Understanding open surfaces of closed loops is important in many fields, such as mathematics, physics, and engineering. These surfaces have unique properties and can be used to model real-world objects and phenomena, such as the Earth's magnetic field or the shape of a spaceship.

5. How can open surfaces of closed loops be visualized?

Open surfaces of closed loops can be visualized in various ways, such as through mathematical equations, computer-generated images, or physical models. These visualizations can help scientists better understand the properties and behavior of these surfaces.

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