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Homework Statement
Homework Equations
The Attempt at a Solution
Jacobian of the coordinate system (## u_1, u_2##) with respect to another coordinate system (x,y ) is given by
J = ## \begin{vmatrix}
\frac { \partial {u_1 } } {\partial {x } } & \frac { \partial {u_1 } } {\partial {y} } \\
\frac { \partial {u_2 } } {\partial {x } } & \frac { \partial {u_2 } } {\partial {y } }\end{vmatrix} ##
Now, ## u_1(x,y), u_2(x,y) = ?##
In polar coordinate system,
## x(r, \theta) = \vec r \cdot \hat x ##
## y(r, \theta) = \vec r \cdot \hat y ##
Applying the same,
## u_1(x,y)= \vec x \cdot \hat u_1 = x ##
## u_2(x,y)= \vec x \cdot \hat u_2 = \frac { k}{\sqrt{ (k^2 x^2 + y^2)}} ##
Thus, I get J as a function of x.
Is this correct?
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