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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.
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Definition of Divergence of a vector field?
hedivergence of a vector fieldF= (F(x,y),G(x,y)) with continuous partial derivatives is defined by:
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.
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 physical quantity use both magnitude and direction?
Any vector quantity does. Examples of vector quantities include but are not limited to . . . - Displacement - Velocity - Acceleration - Torque - Force - Electric field - Momentum - Poynting vector
Is magnetic field line scalar or vector quantity?
Vector.
Definition of Divergence of a vector field?
hedivergence of a vector fieldF= (F(x,y),G(x,y)) with continuous partial derivatives is defined by:
What is transformed divergence?
Transformed divergence is a concept in vector calculus that involves calculating the divergence of a vector field after applying a transformation to the coordinate system. This technique is often used to simplify calculations in complex systems by changing the coordinate system to make the divergence easier to compute.
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.
Continuity equation for time varying field?
The continuity equation for a time-varying field relates the divergence of the field with the rate of change of field strength at any given point. Mathematically, it is expressed as ∇⋅E = -∂ρ/∂t, where ∇ is the divergence operator, E is the field, ρ is the charge density, and ∂/∂t represents the partial derivative with respect to time. This equation ensures that the field and charge distributions are consistent over time, in accordance with the principle of charge conservation.
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 are the example vector?
Examples of vector quantity are displacement, velocity, acceleration, momentum, force, E-filed, B-field, torque, energy, etc.
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 are the examples of vector?
Examples of vector quantity are displacement, velocity, acceleration, momentum, force, E-filed, B-field, torque, energy, etc.
Is curl of vector function F must perpendicular to every vector function f?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
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 physical quantity use both magnitude and direction?
Any vector quantity does. Examples of vector quantities include but are not limited to . . . - Displacement - Velocity - Acceleration - Torque - Force - Electric field - Momentum - Poynting vector
