Wright State University Lake Campus/2017-1/Phy2400

${\vec {F}}\cdot d{\vec {\ell }}=F_{x}dx+F_{y}dy=F_{r}dr+F_{\theta }rd\theta$

proof

${\vec {F}}\cdot d{\vec {\ell }}=\left(F_{x}{\hat {i}}+F_{y}{\hat {j}}\right)\cdot \left({\hat {i}}dx+{\hat {j}}dy\right)$ $=F_{x}dx({\hat {i}}\cdot {\hat {i}})+F_{y}dy({\hat {j}}\cdot {\hat {j}})+(junk)({\hat {j}}\cdot {\hat {i}})$ where ${\hat {i}}\cdot {\hat {i}}={\hat {j}}\cdot {\hat {j}}=1$ and ${\hat {i}}\cdot {\hat {j}}=0$. For polar coordinates, use $d{\vec {\ell }}={\hat {r}}dr+rd\theta {\hat {\theta }}$

NOTE ERROR IN SYLLABUS: Final Exam is MONDAY 4/24/17

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