Recent content by chiyu

Ohhhh I see now! I think I'm 100% clear now, that makes a lot of sense. Thank you for being patient with me.

Ah I think I do now! Am I right in saying then that $$d\mathbf{r}=d\rho~\hat{\rho}+\rho~d\phi~\hat{\phi}+dz~\hat z$$ is the general expression, and if in the specific case where ##\rho## depend on ##\phi##, we can write ##d\rho## as ##\frac{\partial \rho}{\partial \phi} d\phi##, so that will...

But let's say instead of a circle, we take the surface of a oblong cylinder, then depending on the angle the distance will change right?

Hey thanks for your help. I am a bit confused about why ##\rho## doesn't depend on ##\phi##? I get that that is the case for a position vector to any point in space, but if the curve we defined has ##\rho## as a function of ##\phi##, why would it still be the case that the additional term is 0?

We were taught that in cylindrical coodrinates, the position vector can be expressed as And then we can write the line element by differentiating to get . We can then use this to do a line integral with a vector field along any path. And this seems to be what is done on all questions I've...