## What is the divergence of a function?

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Divergence measures the change in density of a fluid flowing according to a given vector field.

**What is the physical significance of divergence?**

The physical significance of the divergence of a vector field is the rate at which “density” exits a given region of space.

### What is divergence of a vector field express it in Cartesian coordinate system?

The rate of change of a vector field is complex. The divergence of a vector field indicates how much the vector field spreads out from a certain point. The divergence of a vector is scalar.

**How do you find the divergence in cylindrical coordinates?**

However, we also know that F ¯ in cylindrical coordinates equals to: F ¯ = ( r cos. . θ, r sin. . θ, z), and the divergence in cylindrical coordinates is the following: ∇ ⋅ F ¯ = 1 r ∂ ( r F ¯ r) ∂ r + 1 r ∂ ( F ¯ θ) ∂ θ + ∂ ( F ¯ z) ∂ z. The big question is: what are F ¯ r, θ, z?

## What is the derivation for the divergence in polar coordinates?

I have already explained to you that the derivation for the divergence in polar coordinates i.e. Cylindrical or Spherical can be done by two approaches. Starting with the Divergence formula in Cartesian and then converting each of its element into the Spherical using proper conversion formulas.

**What is the normal divergence of uniform vector field?**

While if the field lines are sourcing in or contracting at a point then there is a negative divergence. The uniform vector field posses a zero divergence. The Divergence formula in Cartesian Coordinate System viz. the normal Divergence formula can be derived from the basic definition of the divergence.

### Why are cylindrical and spherical unit vectors not the same?

Because cylindrical and spherical unit vectors are not universally constant. Though their magnitude is always 1, they can have different directions at different points of consideration. So unlike the cartesian these unit vectors are not global constants. Read: Derivatives of the unit vectors in different coordinate systems.