IGNOU PHE 4 2018 - Express the vector field F = xzˆi + (x2 + y 2 )ˆj + (x/z)k i

Question

Express the vector field F = xzˆi + (x2 + y 2 )ˆj + (x/z)k in cylindrical polar coordinates.

25 Jan 2018

Answer :

Word Count : 372

To solve for the vector field \( \mathbf{F} \) in cylindrical polar coordinates, we need to express the given Cartesian components of the vector field in terms of the cylindrical polar coordinates \( (r, \theta, z) \). The relations between Cartesian and cylindrical coordinates are: \[ x = r \cos\theta, \quad y = r \sin\theta, \quad z = z \] and the unit vectors in cylindrical coordinates are: \[ \hat{i} = \cos\theta \hat{r} - \sin\theta \hat{\theta}, \quad \hat{j} = \sin\theta \hat{r} +

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