- #1
barnflakes
- 156
- 4
Express the following vector field in spherical coordinates. (The
answer should be in a form that uses the unit vectors of the curvilinear coordi-
nate system and coefficient functions that are written in terms of the curvilinear
coordinates.)
[itex] \underline{F} = -y \underline{i} + x \underline{j} + (x^2 + y^2)\underline{k}[/itex]
OK, so I've obtained the equation:
[itex]\underline{F} = rsin\theta(-sin\phi\mathbf{i} + cos\phi\underline{j} +rsin\theta\underline{k})[/itex] simply by substituting [itex]x = rsin\theta cos\phi[/itex] etc. into the above equations. Now how do I express this in terms of the unit vectors [itex]\mathbf{e}_r,\mathbf{e}\phi, \mathbf{e}_\theta[/itex] ??
answer should be in a form that uses the unit vectors of the curvilinear coordi-
nate system and coefficient functions that are written in terms of the curvilinear
coordinates.)
[itex] \underline{F} = -y \underline{i} + x \underline{j} + (x^2 + y^2)\underline{k}[/itex]
OK, so I've obtained the equation:
[itex]\underline{F} = rsin\theta(-sin\phi\mathbf{i} + cos\phi\underline{j} +rsin\theta\underline{k})[/itex] simply by substituting [itex]x = rsin\theta cos\phi[/itex] etc. into the above equations. Now how do I express this in terms of the unit vectors [itex]\mathbf{e}_r,\mathbf{e}\phi, \mathbf{e}_\theta[/itex] ??