Direction of Magnetic Field for a Charged Rotating Disc

In summary, the rotating disc produces a magnetic field with two components, \hat{r} and \hat{\theta}, and the direction of the field depends on where it is being measured, with the field lines resembling those of a circular loop of current.
  • #1
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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?
 
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  • #2
The cross product will give you the direction.
 
  • #3
Rahmuss said:

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
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
Rahmuss said:
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.
 

1. What is the direction of the magnetic field for a charged rotating disc?

The direction of the magnetic field for a charged rotating disc depends on the direction of rotation and the orientation of the disc's axis. If the disc is rotating counterclockwise when viewed from above, the magnetic field will be directed into the disc. If the disc is rotating clockwise, the magnetic field will be directed out of the disc.

2. How does the direction of rotation affect the magnetic field?

The direction of rotation is directly linked to the direction of the magnetic field. If the disc is rotating in one direction, the magnetic field will be directed in the opposite direction. This is known as the right-hand rule, where the direction of the magnetic field is perpendicular to the direction of current flow.

3. Does the charge of the disc affect the direction of the magnetic field?

Yes, the charge of the disc affects the direction of the magnetic field. If the disc has a positive charge, the magnetic field will be directed in one direction. If the disc has a negative charge, the magnetic field will be directed in the opposite direction. This is because charged particles in motion create a magnetic field.

4. How does the orientation of the disc's axis affect the direction of the magnetic field?

The orientation of the disc's axis determines the direction of the magnetic field. If the disc's axis is perpendicular to the direction of rotation, the magnetic field will be directed into or out of the disc. If the axis is parallel to the direction of rotation, the magnetic field will be directed along the axis.

5. Can the direction of the magnetic field be changed?

Yes, the direction of the magnetic field can be changed by altering the direction of rotation, the charge of the disc, or the orientation of the disc's axis. Additionally, an external magnetic field can also be used to change the direction of the magnetic field of a charged rotating disc.

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