Bounding Surface of Volume Integral: Sphere at Origin

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In summary, there is confusion about the definition of a bounding surface and how it relates to integrating over a region where the radius is greater than "a". The explanation in Greiner Classical Electrodynamics states that the bounding surface of the volume is a sphere, but it is unclear if this means the integration was done over the sphere or not. Further clarification is needed.
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Homework Statement



Say I have a sphere at the origin with radius "a". If I am integrating over a region in which r is greater than "a", how can the bounding surface of this volume be the spherical surface? This comes from an explanation in Greiner Classical Electrodynamics, in which he says the volume integral was done in a region such that r is greater than "a", but at the same time he says the bounding surface of this volume is the sphere...


The Attempt at a Solution



I feel like I am missing something on the defintion of a bounding surface, but the only definition I can find is the one that says that it is the surface that "binds" the whole volume. Hence, the spherical surface at "a" might be a part of the surface that is part of the volume "v", but there should be more, since the integration wasn't done over the sphere.

Any help will be appreciated.

Thanks
 
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  • #2
Maybe you integrate from a<R<r , But I am not sure
 

1. What is the bounding surface of a volume integral?

The bounding surface of a volume integral refers to the surface that encloses the region over which the integral is being evaluated. It is used to calculate the volume of a solid object or the total mass of a continuous object.

2. What is the purpose of using a bounding surface in a volume integral?

The purpose of using a bounding surface in a volume integral is to define the limits of integration and to ensure that the integral is only evaluated over the desired region. It also helps to simplify the calculation and make it more manageable.

3. What is the most commonly used bounding surface in volume integrals?

The most commonly used bounding surface in volume integrals is a sphere at the origin. This is because it is a symmetrical shape that is easy to work with and can be used to evaluate a wide range of integrals.

4. How is the bounding surface of a volume integral related to the concept of flux?

The bounding surface of a volume integral is closely related to the concept of flux, which is the flow of a physical quantity through a surface. In volume integrals, the bounding surface is used to calculate the flux of a vector field through a region.

5. Can the bounding surface in a volume integral be any shape?

Yes, the bounding surface in a volume integral can be any shape as long as it completely encloses the region of integration. However, certain shapes may be more convenient to work with and may lead to simpler calculations.

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