Derivative of basis vectors

  • #1

Homework Statement


I am unsure as to how the partial derivative of the basis vector e_r with respect to theta is (1/r)e_theta in polar coordinates

Homework Equations




The Attempt at a Solution


differentiating gives me -sin(theta)e_x+cos(theta)e_y however I'm not sure how to get 1/r.
 

Answers and Replies

  • #2
vela
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You shouldn't get a factor of 1/r. Why do you think there is one?
 
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  • #3
Orodruin
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You shouldn't get a factor of 1/r. Why do you think there is one?
Based on some of his other threads, he is not using normalised basis vectors but ##\vec e_i = \partial_i \vec x## (which I usually would denote ##\vec E_i## or similar to underline that they are not necessarily unit vectors - however, there are some places in the literature where ##\vec e_i## is used and instead ##\hat i## or similar is used for normalised basis vectors). With my preferred notation, where ##\vec e_i## are normalised and ##\vec E_i = \partial_i \vec x##, you would have ##\vec E_r = \vec e_r## but ##\vec E_\theta = r \vec e_\theta## so indeed you would have ##\partial_\theta \vec E_r = \vec E_\theta/r##.
 

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