Question

5A

Research and share two or more real life applications of radial, rotational, or gradient fields.

5B

Explain the concept of divergence and provide an example showing how to calculate the divergence of the vector field chosen in your example.

Answer 1

The gradient is a slope the divergene measures the spreading out of fields the cure measures the circulation of fields · » The example for the liradial fields" Think of water coming from a forest. =) Imagine a fluid with a vector field representing the velocity of the fluid at each point in space. Divergence measures the flow of fluid out of a point - gravitational, electric fields are also examples. The rotational field think of rotating water in bucket has core. You can measure cord loy putting a piece at dust in the liquid and seeing it . at spins around its own .داده - ->) Tornado, whirlpool abo examples of rotational field. gradient field is 1 scalar field'. example of the field that given the elevation of the ground above sea level at given point on the earth.

a da - Used in fluid simulations: - Recall from the divergence of vector y field page that if F(Q, y, z)= P(X,Y, 7) { +(2,4, 2); +R(2,,7) k. » is vector field on R and if op op - all earst, Then the divergence of f is given by the following formula. div (F) = OFF thang F (1,3,7) = 2x e*yi tag cos aš – (y+z) P= Qxe*y; & = xy?cosz ; R3 = (4+2) (23e+y) = 24 (ge*+ex) og - gay ; =-) Thos, divergence is poft des sa = 2e y(x+1)+22y-. Example: