What is the physical significance of Stokes theorem?

Explanation: 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. Hope this heled you!

Which one is right interpretation of Stokes theorem?

The Stoke’s theorem states that “the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface.”

What is the physical meaning of divergence theorem?

The divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into or away from the region through its boundary.

What are the applications of Stokes theorem?

Physical applications of Strokes’ theorem. Sufficient conditions for a vector field to be conservative. Stokes’ theorem gives a relation between line integrals and surface integrals. Depending upon the convenience, one integral can be computed interms of the other.

What are the limitations of Stokes theorem?

When the solid content of a suspension is high, Stokes’ equation may not show the real sedimentation rate. High solid content imparts additional viscosity to the system, which must be taken into consideration if the correct rate of settling is to be determined. The equation contains only the viscosity of the medium.

How do you evaluate Stokes theorem?

Stokes’ theorem can be used to transform a difficult surface integral into an easier line integral, or a difficult line integral into an easier surface integral. Through Stokes’ theorem, line integrals can be evaluated using the simplest surface with boundary C.

What is the physical significance of divergence and curl of a vector?

Key Concepts The divergence of a vector field is a scalar function. Divergence measures the “outflowing-ness” of a vector field. If v is the velocity field of a fluid, then the divergence of v at a point is the outflow of the fluid less the inflow at the point. The curl of a vector field is a vector field.

What do you mean by divergence of vector field discuss its geometrical interpretation and physical significance?

The divergence of a vector field simply measures how much the flow is expanding at a given point. It does not indicate in which direction the expansion is occuring. Hence (in contrast to the curl of a vector field), the divergence is a scalar.

What are the conditions 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 are the necessary conditions for 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.

What is the intuition behind Stokes theorem?

Stokes’ Theorem:Physical intuition Stokes’ theorem is a more general form of Green’s theorem. Stokes’ theorem states that the total amount of twisting along a surface is equal to the amount of twisting on its boundary. Suppose we have a hemisphere and say that it is bounded by its lower circle.

What do Stokes’ and green’s theorems represent?

Green and Stokes’ Theorems are generalizations of the Fundamental Theorem ofCalculus, letting us relate double integrals over 2 dimensional regions to singleintegrals over their boundary; as you study this section, it’s very important totry to keep this idea in mind. They will allow us to compute many integralsthat arise in real life situations, and give us a much deeper understanding of therelationship between multivariate forms of the derivative and integrals.

What is the mean speed theorem?

Mean speed theorem. It essentially says that: a uniformly accelerated body (starting from rest, i.e., zero initial velocity) travels the same distance as a body with uniform speed whose speed is half the final velocity of the accelerated body.

What is the cosine theorem?

Cosine theorem. The square of a side of a triangle is equal to the sum of the squares of the other two sides, minus double the product of the latter two sides and the cosine of the angle between them: Here are the sides of the triangle and is the angle between and .