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\textbf{Vector Fields}

\textit{\textbf{Scalar and Vector Fields}}
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\textbf{Question}

Determine the field lines of the following polar vector field.

$\un{F} = 2\un{\hat{r}} + \theta\un{\hat{\theta}}$


\textbf{Answer}

The field lines satisfy $\frac{dr}{2} = r\frac{d\theta}{\theta}$, or
$\frac{dr}{r} = 2\frac{d\theta}{\theta}$.

So the field lines are the spirals $r = C\theta^2$.


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