Uniformly Charged Circular Disk

In summary, the electric field does not point in the r, θ, or z directions around a uniformly charged disk. This is because symmetry arguments suggest that all directions should be treated equally. The problem likely refers to the direction outside of the disk, where the disk appears to be a point.
  • #1
cheungw
1
0

Homework Statement


In what direction (using cylindrical coordinates) around a uniformly disk does the electric field NOT point?


Homework Equations


The directions could be r, θ, or z.


The Attempt at a Solution


I don't think it can point in the θ or the z direction-- either one would imply that there is a built-in preference to space for a certain direction, because symmetry arguments say that these two directions should be treated equally in all directions.

I'm not sure though-- I'm assuming they mean around the edge of the disk on the outside, is this correct?
 
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  • #2
cheungw said:

Homework Statement


In what direction (using cylindrical coordinates) around a uniformly disk does the electric field NOT point?

Homework Equations


The directions could be r, θ, or z.

The Attempt at a Solution


I don't think it can point in the θ or the z direction-- either one would imply that there is a built-in preference to space for a certain direction, because symmetry arguments say that these two directions should be treated equally in all directions.

I'm not sure though-- I'm assuming they mean around the edge of the disk on the outside, is this correct?
Hello cheungw. Welcome to PF !

What if they don't mean around the edge of the disk ?

What if they mean in the vicinity of the disk ?
 
  • #3
cheungw said:

Homework Statement


In what direction (using cylindrical coordinates) around a uniformly disk does the electric field NOT point?


Homework Equations


The directions could be r, θ, or z.


The Attempt at a Solution


I don't think it can point in the θ or the z direction-- either one would imply that there is a built-in preference to space for a certain direction, because symmetry arguments say that these two directions should be treated equally in all directions.

I'm not sure though-- I'm assuming they mean around the edge of the disk on the outside, is this correct?

The problem says "around" the disk, so that probably means where does E not point outside of the disk.

to answer, consider the electric field in regions far far away from the disk, so that the disk appears to be a point. What would the field look like?
 

What is a uniformly charged circular disk?

A uniformly charged circular disk is an object with a flat, circular shape and a constant distribution of electric charge on its surface.

How is the electric field calculated for a uniformly charged circular disk?

The electric field at a point on the axis of a uniformly charged circular disk can be calculated using the formula E = (σ / 2ε0) * (1 - (z / √(z2 + R2))), where σ is the surface charge density, ε0 is the permittivity of free space, z is the distance from the center of the disk, and R is the radius of the disk.

What is the difference between a uniformly charged circular disk and a point charge?

A uniformly charged circular disk has a finite size and a continuous distribution of charge, while a point charge is an infinitesimally small particle with a discrete amount of charge. Additionally, the electric field of a point charge follows an inverse square law, while the electric field of a uniformly charged circular disk follows a more complex formula.

How does the electric potential vary on the surface of a uniformly charged circular disk?

The electric potential on the surface of a uniformly charged circular disk is constant, as the electric field is perpendicular to the surface and therefore does no work on a charged particle moving along the surface.

What are some real-world applications of a uniformly charged circular disk?

A uniformly charged circular disk can be used in capacitors, where it is paired with another charged object to store electrical energy. It can also be used in particle accelerators to manipulate the trajectory of charged particles. In addition, it can be used in surface charge measurements and in electrostatic printing.

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