Question

Given the vector \textbf{F} = -y\hat{\textbf{i}} + x\hat{\textbf{j}} in Cartesian coordinates, write down the vector's representation in spherical coordinates. That is the vector should be written in terms of the coordinates r, $\theta$, $\phi$ and the spherical unit vectors $\hat{\textbf{r}}$, $\hat{\theta}$, $\hat{\phi}$. You may either submit this online or submit a paper copy in class. [3 points]

          Given the vector
\textbf{F} = -y\hat{\textbf{i}} + x\hat{\textbf{j}}
in Cartesian coordinates, write down the vector's
representation in spherical coordinates. That is the
vector should be written in terms of the coordinates
r, $\theta$, $\phi$ and the spherical unit vectors $\hat{\textbf{r}}$, $\hat{\theta}$, $\hat{\phi}$. You may
either submit this online or submit a paper copy in
class. [3 points]

Given the vector
F = -yî + xĵ
in Cartesian coordinates, write down the vector's
representation in spherical coordinates. That is the
vector should be written in terms of the coordinates
r, θ, ϕ and the spherical unit vectors r̂, θ̂, ϕ̂. You may
either submit this online or submit a paper copy in
class. [3 points]

Added by Marcos H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

09/01/2023

Step 1

To convert from Cartesian coordinates (x, y) to spherical coordinates (r, θ, φ), we can use the following equations: r = √(x^2 + y^2) θ = arctan(y/x) φ = arctan(√(x^2 + y^2)/z) In this case, we have F = -yi + xj. So, x = 0 and y = -1. Show more…

Show all steps

Thanks for your feedback!

Please help me out. Given the vector F = -yi + xj in Cartesian coordinates, write down the vector's representation in spherical coordinates. That is, the vector should be written in terms of the coordinates r and the spherical unit vectors r. You may either submit this online or submit a paper copy in class. [3 points]