Problem-Solving: Fall-2025
W2 D1 Practice : Due W2 D1
- Vector Field Fit
S0 5401S
Consider the vector field \(\boldsymbol{\vec F}\) shown. Which of the following formulas best fits \(\boldsymbol{\vec F}\)? Why? \begin{align*} \hbox{(a)}~~\boldsymbol{\vec F}_1 &= \frac{x}{x^2+y^2}\>\boldsymbol{\hat x} + \frac{y}{x^2+y^2}\>\boldsymbol{\hat y} \cr \hbox{(b)}~~\boldsymbol{\vec F}_2 &= -y\,\boldsymbol{\hat x} + x\,\boldsymbol{\hat y} \cr \hbox{(c)}~~\boldsymbol{\vec F}_3 &= \frac{-y}{(x^2+y^2)^2}\>\boldsymbol{\hat x} + \frac{x}{(x^2+y^2)^2}\>\boldsymbol{\hat y} \end{align*}