Why does the current have no ##\phi## component in a toroidal coil?

[rude man]

But in spite of all these I can't seem to understand how the current have no $\phi$ component. Well, in that toroid we have current going on in circles and really I don't anything more than this.

Please help me!

You can make the $\phi$ component of current = 0 by the way you wind the wire.

If you use just one winding then obviously there must be a $\phi$ component of current since each turn of wire is connected to the next by a short run of $\phi$ section to get around the toroid's periphery.

But if you do 2 windings (layers) the second winding's sections' current can cancel out the first if properly wound.

 

[Adesh]

You can make the $\phi$ component of current = 0 by the way you wind the wire.

If you use just one winding then obviously there must be a $\phi$ component of current since each turn of wire is connected to the next by a short run of $\phi$ section to get around the toroid's periphery.

But if you do 2 windings (layers) the second winding's sections' current can cancel out the first if properly wound.

Yes, I got it thanks. You know my main problem was that I was unable to decompose a circle (that is the loop of a wire wound around the toroid) into just $\hat{r}$ and $\hat{z}$ components, because you know when we draw a circle in $xy$ plane we decompose it’s line elements into $\hat{r}$ and $\hat{\phi}$ directions (if we use polar coordinates) . So, it was hard for me to imagine such a situation where we had no $\phi$ component.

 

[rude man]

Yes, I got it thanks. You know my main problem was that I was unable to decompose a circle (that is the loop of a wire wound around the toroid) into just $\hat{r}$ and $\hat{z}$ components, because you know when we draw a circle in $xy$ plane we decompose it’s line elements into $\hat{r}$ and $\hat{\phi}$ directions (if we use polar coordinates) . So, it was hard for me to imagine such a situation where we had no $\phi$ component.

Right. The trick is two windings with the second nulling the $\phi$ component from the first.