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I need help. The topic is a gradient in spherical coordinates. In cartesian it is clear but in spherical coordinates I have two terms which I don't understand from where they come.

Okay, I have a scalar field in spherical coordinates:

[tex] \Phi = \Phi(r, \theta, \phi) [/tex]

I thought that this is the gradient but it is wrong and I don't know why :(

[tex] grad \Phi = \frac{\partial \phi}{\partial r} \vec{e}_{r} + \frac{\partial \phi}{\partial \theta} \vec{e}_{\theta} + \frac{\partial \phi}{\partial \phi} \vec{e}_{\phi}[/tex]

My mathbook tells me that this is the gradient in spherical coordinates but I don't understand the terms [tex] \frac{1}{r} [/tex] and [tex] \frac{1}{r \sin(\theta)} [/tex]

[tex] grad \Phi = \frac{\partial \phi}{\partial r} \vec{e}_{r} + \frac{1}{r} ~ \frac{\partial \phi}{\partial \theta} \vec{e}_{\theta} + \frac{1}{r \sin(\theta)} ~ \frac{\partial \phi}{\partial \phi} \vec{e}_{\phi}[/tex]

I would be thank you for helping :)

greetings

P.S.

Sorry for my bad english. I will practice and learn grammar for better english in the future ;)

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# Gradient in spherical coordinates problem

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