• Support PF! Buy your school textbooks, materials and every day products Here!

Direction of Magnetic Field for a Charged Rotating Disc

  • Thread starter Rahmuss
  • Start date
  • #1
222
0

Homework Statement


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.


Homework Equations


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


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?
 

Answers and Replies

  • #2
1,482
3
The cross product will give you the direction.
 
  • #3
gabbagabbahey
Homework Helper
Gold Member
5,002
6

Homework Statement


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.


Homework Equations


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


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?
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.
 
  • #4
222
0
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?
 
  • #5
gabbagabbahey
Homework Helper
Gold Member
5,002
6
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?
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.
 

Related Threads for: Direction of Magnetic Field for a Charged Rotating Disc

Replies
7
Views
882
Replies
1
Views
2K
  • Last Post
Replies
1
Views
845
  • Last Post
Replies
4
Views
3K
Replies
4
Views
4K
  • Last Post
Replies
1
Views
957
Replies
1
Views
1K
Replies
0
Views
6K
Top