Why is the flux through the top of a cylinder zero?

In summary, the flux through the top of a cylinder is a measure of the flow of a vector field through the surface of the cylinder and is represented by the symbol Φ. It is important in understanding vector field behavior and is used in engineering and scientific applications. The flux through the top of a cylinder is zero when the surface is parallel to the vector field, but can be non-zero if the surface is not parallel. It is calculated using the formula Φ = E∙A∙cosθ, based on the dot product of the vector field and the surface normal vector.
  • #1
Sam Anderson
4
0
This is example 27.2 in my textbook. I have the answer, but it doesn't make sense to me. I understand that if electric field is tangent to the surface at all points than flux is zero. Why, though, does my textbook assume that the ends of the cylinder don't have field lines extending upwards and downwards, out of the top and bottom of the cylinder?
 
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  • #2
What textbook? It's important to know what kind of charge distribution you have inside the cylinder and how it's positioned.
 

What is flux through the top of a cylinder?

The flux through the top of a cylinder is a measure of the flow of a vector field, such as electric or magnetic fields, through the surface of the cylinder. It is represented by the symbol Φ and is measured in units of volt-meters or webers.

Why is the flux through the top of a cylinder important?

The flux through the top of a cylinder is important because it helps us understand the behavior of vector fields and their interactions with different surfaces. It is also used in various engineering and scientific applications, such as calculating the strength of an electric or magnetic field.

Why is the flux through the top of a cylinder zero?

The flux through the top of a cylinder is zero because the surface area of the top of the cylinder is parallel to the direction of the vector field. This means that the field lines do not intersect the surface, resulting in no flow through the surface and therefore a flux of zero.

Can the flux through the top of a cylinder ever be non-zero?

Yes, the flux through the top of a cylinder can be non-zero if the surface is not parallel to the direction of the vector field. In this case, the field lines intersect the surface and there is a flow of the vector field through the surface, resulting in a non-zero flux.

How is the flux through the top of a cylinder calculated?

The flux through the top of a cylinder can be calculated using the formula Φ = E∙A∙cosθ, where E is the strength of the vector field, A is the area of the surface, and θ is the angle between the vector field and the surface. This formula is based on the dot product of the vector field and the surface normal vector.

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