Direction of Magnetic Field for a Charged Rotating Disc

Rahmuss

1. The problem statement, all variables and given/known data
The question actually asks for the equation for the magnetic field for the rotating disc; but all I'm after is the direction of the magnetic field.


2. Relevant equations
None were given; but I've been using:
[tex] \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}[/tex]


3. The attempt at a solution
When I use the above equation I get two components to the magnetic field: [tex]\hat{r}[/tex] and [tex]\hat{\theta}[/tex]. That doesn't really make a lot of sense to me. What am I missing?

waht

The cross product will give you the direction.

gabbagabbahey

The direction of the field depends on where you are measuring it at. If you measure the field along the axis of the disk (presumably the z-axis--- where [itex]\theta=0[/itex]), then the field should point along the axis (assuming the disk is uniformly charged). It may help you to note that [itex]\hat{z}=\cos\theta\hat{r}-\sin\theta\hat{\theta}=\hat{r}[/itex] along the z-axis.

Rahmuss

waht - Thanks. And that part I understand just fine. There is only a z-component of the electric field, so when I do a cross product, I get both an r-component and a theta-component.

gabbagabbahey - So the way you're describing it, the magnetic field seems to come up at the center of the disk, and then moves out and around to the bottom circling back up along the z-axis again?

gabbagabbahey

Yes, the field lines are very similar to those of a circular loop of current. After all, the disk can be thought of as a superposition of a very large number of thin circular loops of various radii.