What are the applications of Stokes theorem?
Stokes’ Theorem is applied to derive the retarded vector potential of loop antennas for the radiation of electric field and magnetic field. Simulations of the ideal and the actual magnetic dipole antenna suggest a satisfactory agreement of the two antennas.
What is the physical significance of Stokes theorem?
Stoke’s Theorem relates a surface integral over a surface to a line integral along the boundary curve. In fact, Stokes’ Theorem provides insight into a physical interpretation of the curl.
Which operation is used in Stokes theorem?
curl operation
Explanation: ∫A. dl = ∫∫ Curl (A). ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.
Which of the following represent statement of Stokes theorem?
Stoke’s theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.
Who invented Stokes theorem?
It is named after Sir George Gabriel Stokes (1819–1903), although the first known statement of the theorem is by William Thomson (Lord Kelvin) and appears in a letter of his to Stokes in July 1850. The theorem acquired its name from Stokes’s habit of including it in the Cambridge prize examinations.
When can you not use Stokes theorem?
Stokes theorem does not always apply. The first condition is that the vector field, →A, appearing on the surface integral side must be able to be written as →∇×→F, where →F would either have to be found or may be given to you. If →F cannot be found, then Stokes theorem cannot be used.
What are the requirements for Stokes theorem?
Stokes’ Theorem is about tiny spirals of circulation that occurs within a vector field (F). The vector field is on a surface (S) that is piecewise-smooth. Additionally, the surface is bounded by a curve (C). The curve must be simple, closed, and also piecewise-smooth.
What is stokes law derive the relation of it by using dimensions?
He found what has become known as Stokes’ Law: the drag force F on a sphere of radius a moving through a fluid of viscosity η at speed v is given by: F=6πaηv. Note that this drag force is directly proportional to the radius…..
What is the formula for Stokes theorem?
By Stokes’ theorem, ∬S1curl⇀F⋅d⇀S=∫C⇀F⋅d⇀r=∬S2curl⇀F⋅d⇀S.
What is the boundary in Stokes theorem?
The required relationship between the curve C and the surface S (Stokes’ theorem) is identical to the relationship between the curve C and the region D (Green’s theorem): the curve C must be the boundary ∂D of the region or the boundary ∂S of the surface.
Can Stokes theorem be applied to closed surfaces?
Because it is equal to a work integral over its boundary by Stokes’ Theorem, and a closed surface has no boundary!
What are the limitations of stokes law?
Limitations of Stokes’ Law Some colloidal particles of the same mass fall slower than others due to the difference in the shapes of particles. Many fast-falling particles may drag finer particles down along with them.
What is stokes law in chemical engineering?
Stoke’s Law is an equation that expresses the settling velocities of small spherical particles in a fluid medium. The law is established by taking into account the forces acting on a certain particle as it falls through a liquid column under the influence of gravity.
What factors affect Stokes law?
Stoke’s Law Derivation The viscous force acting on a sphere is directly proportional to the following factors: Coefficient of viscosity (η). The radius of the sphere (r). The velocity of the object (v).
What are the four conditions of Stokes law?
Explanation: 1) The law applies to a fluid of infinite extent . 2) The law does not hold good if the spherical body is moving so fast that conditions are not streamline. 3) The spherical body must be rigid and smooth .
What is Stokes law and its two applications?
We use Stoke’s law to determine the terminal velocity, the size and the density of sphere and liquid, respectively. Stoke’s law can also be used to calculate the viscosity of the fluid.