Vector Field A Analysis Homework Answers Needed

Your Question:

$\[ \begin{array}{c} \mathrm{P}(\mathrm{r}, \phi, \mathrm{z})=\mathrm{P}\left(2,45^{\circ}, 5\right) \\ A=4 \sin \phi \hat{r}+$

Answer the following questions according to the vector field A and points P given above.

Step By Step Answers with Explanation

a) Calculate the vector field A at the point P in Cylindrical coordinates:

To express the vector field A in cylindrical coordinates (ρ, θ, z), we'll need to convert the given Cartesian expression into cylindrical coordinates. The cylindrical coordinates for point P(r, θ, z) are (4, 45°, 5). The vector field A in cylindrical coordinates is:

x = ρ * cos(θ)

y = ρ * sin(θ)

x = 4 * cos(45°) = 2√2

y = 4 * sin(45°) = 2√2

The point P is given in cylindrical coordinates as (ρ, θ, z) = (4, 45°, 5). We can use the conversion formulas mentioned earlier to express this point in Cartesian coordinates:

x = ρ * cos(θ) = 4 * cos(45°) = 2√2

We have already expressed the vector field A in Cartesian coordinates in part (b):

A(x, y, z) = -4√2cos(76)