infinitesimal element उदाहरण वाक्य

For a volume charge distribution ( such as charge within a bulk metal ) where gives the charge per unit volume at position, and is an infinitesimal element of volume,
For a linear charge distribution ( a good approximation for charge in a wire ) where gives the charge per unit length at position, and is an infinitesimal element of length,
For a surface charge distribution ( a good approximation for charge on a plate in a parallel plate capacitor ) where gives the charge per unit area at position, and is an infinitesimal element of area,
From equilibrium of forces on the infinitesimal element, the magnitudes of the normal stress \ sigma _ \ mathrm { n } and the shear stress \ tau _ \ mathrm { n } are given by:
Nelson's formulation is made more accessible for the lay-mathematician by leaving out many of the complexities of meta-mathematical logic that were initially required to justify rigorously the consistency of number systems containing infinitesimal elements.

The model consists of an " infinite series " of the infinitesimal elements shown in the figure, and that the values of the components are specified " per unit length " so the picture of the component can be misleading.
With a horizontal movement or two, we can find a way to the surface, so we might as well integrate over z after all . ( The container is not symmetrical, but all that fluid mechanics requires is local symmetry : each infinitesimal element of fluid is symmetrical .)
For a volume charge distribution ( such as charge within a bulk metal ) where \ rho ( \ mathbf { r ^ \ prime } ) gives the charge per unit volume at position \ mathbf { r ^ \ prime }, and dV ^ \ prime is an infinitesimal element of volume,
For a linear charge distribution ( a good approximation for charge in a wire ) where \ lambda ( \ mathbf { r ^ \ prime } ) gives the charge per unit length at position \ mathbf { r ^ \ prime }, and dl ^ \ prime is an infinitesimal element of length,
For a surface charge distribution ( a good approximation for charge on a plate in a parallel plate capacitor ) where \ sigma ( \ mathbf { r ^ \ prime } ) gives the charge per unit area at position \ mathbf { r ^ \ prime }, and dA ^ \ prime is an infinitesimal element of area,