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What is physical significance of divergence?
Divergence is a vector operator that measures the magnitude of a vector fields source or sink at a given point.
Examples of divergence of a vector field?
I am not sure if this is the answer you are looking for, since the question is listed in both Physics and Abstract Algebra, so I will try to give you some examples from physics. One of the indicators of a divergence of a vector field is the presence of a source. For example the electric field can be represented by a vector field, with each vector pointing along the field and has a length proportional to the strength of the electric field at that position. A point source then causes an electric field with a divergence at the location of the point source, with the vectors all pointing away from it (positive charge) or towards it (negative charge). Another example would be some point mass and the Newtonian gravitational field. One of Maxwell's equations states that the magnetic field cannot have any divergences meaning that there are no magnetic monopoles.
How does vector calculus apply in fluid mechanics?
The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.
Is magnetic field line scalar or vector quantity?
Vector.
The direction of the electric field vector is defined as?
Direction of the electric field vector is the direction of the force experienced by a charged particle in an external electric field.
What is physical significance of divergence?
Divergence is a vector operator that measures the magnitude of a vector fields source or sink at a given point.
Examples of divergence of a vector field?
I am not sure if this is the answer you are looking for, since the question is listed in both Physics and Abstract Algebra, so I will try to give you some examples from physics. One of the indicators of a divergence of a vector field is the presence of a source. For example the electric field can be represented by a vector field, with each vector pointing along the field and has a length proportional to the strength of the electric field at that position. A point source then causes an electric field with a divergence at the location of the point source, with the vectors all pointing away from it (positive charge) or towards it (negative charge). Another example would be some point mass and the Newtonian gravitational field. One of Maxwell's equations states that the magnetic field cannot have any divergences meaning that there are no magnetic monopoles.
Continuity equation for time varying field?
The Continuity Equation for a time varying field Eris:dEr/cdt = Del.Ev where Ev is the vector field associated with the real time varying field.Er + Ev =E, constitute a quaternion field.Del.Ev is the Divergence of the vector field.The Continuity Equation is a statement that the time variation of the real field is equal to the Divergence of the vector field. or more succinctly, the quaternion field E=Er + Ev is Real invariant.The Vector part of the variation is 0= dEv/cdt + Del Er + DelxEv , this is Vector Invariance of E. This is not the Continuioty Equatin but the Induction Equation. Together they represent the Invariance of the quaternion field E=Er + Ev.Because quaternions are not taught in schools yet, few realize the relationship between Continuity and Induction, they are the Real and Vector parts of Invariance!
What is the difference between curl and divergence?
Divergence: rate of spread of vector in free space for non closed path. and Curl: rate of spread of vector in free space for closed path.
What is the reason for the presence of residual magnetism in the field poles?
I'm not quite sure what you're asking, but the reason that there is magnetism at the poles has to do with the fact that magnetic field vector lines have no beginning or end, which is described mathematically through Maxwell's equations; specifically through Gauss' law for magnetism which states that the divergence of a magnetic field is 0, or ∇ ● B = 0. Divergence is a term meaning how much of something is exiting an enclosed surface. Since the divergence of a magnetic field is zero, there must be, always, the exact same amount of magnetic field exiting a surface as entering it, leaving the net divergence as 0.Thus, a magnetic field vector line has to "exit" from somewhere and loop around to "enter" somewhere else, and these two "somewheres" have to be connected (like a circuit). We call these two "somewheres" the magnetic poles.
What is the formula of the divergence of the function?
The divergence of the function is generally a cross product of partial derivatives and the vector field of F. Mathematically, the formula is: div(F) = ∂P/∂x i + ∂Q/∂y j + ∂R/∂z k where: F = Pi + Qj + Rk has the continuous partial derivatives.
How does vector calculus apply in fluid mechanics?
The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.
What has the author Urve Kangro written?
Urve Kangro has written: 'Divergence boundary conditions for vector helmholtz equations with divergence constraints' -- subject(s): Boundary conditions, Helmholtz equations, Coercivity, Boundary value problems, Divergence
What is definition of vector?
A vector is a quantity with both a direction and magnitude
Is magnetic field line scalar or vector quantity?
Vector.
Is field vector quantity?
no
Current is scaler or vector?
Scaler. The electric field is its vector counterpart.
