Static Fields: Winter-2025
HW 05 Practice : Due 1/21 Tues

1. Vector Field Fit S0 5168S

   

   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*}

2. Vector Sketch (Rectangular Coordinates) S0 5168S Sketch each of the vector fields below.
   1. \(\boldsymbol{\vec F} =-y\,\boldsymbol{\hat x} + x\,\boldsymbol{\hat y}\)
   2. \(\boldsymbol{\vec G} = x\,\boldsymbol{\hat x} + y\,\boldsymbol{\hat y}\)
   3. \(\boldsymbol{\vec H} = y\,\boldsymbol{\hat x} + x\,\boldsymbol{\hat y}\)