Electric Field at a Point on the Axis of a Charged Disk?

In summary, the problem involves a charged flat circular annulus with a hole in the center. The surface charge density varies with radial distance from the center of the disk and is given by the equation sigma= (r2 + 961)1/2 x 10-6. The task is to find the magnitude of the electric field at a point on the axis of the disk, 31 m away from the center. To solve this, the equations need to be combined and integrated from 2 to 7. However, there is confusion about the given equation and its units. The correct form of the equation is (sqrt (r squared + 961)) x 10^-6, with r squared in meters and 961 in
  • #1
smballer23
2
0

Homework Statement


A flat, circular annulus of radius 7 m with a hole in the center of radius 2 m is charged on one surface such that the surface charge density varies with the radial distance from the center of the disk by the equation sigma= (r2 + 961)1/2 x 10-6, where is in C/m2 and r is in meters.

Find the magnitude of the electric field at a point on the axis of the disk, a distance 31 m away from the center of the disk.

Homework Equations

disk8.gif

The Attempt at a Solution



Do I combine the equations and integrate from 2 to 7? I am lost...
 
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  • #2
You write: "sigma= (r2 + 961)1/2 x 10-6". Please clarify. Is that r2 or r2? Is 961 in units of meters or meters2? Is that (r2 + 961) x 1/(2 x 10-6), or is it (r2 + 961) x (1/2) x 2 x 10 - 6? Or something else?
 
  • #3
r2 is r squared. 961 is meters.
It is (sqrt(r squared + 961))e-6.
 

FAQ: Electric Field at a Point on the Axis of a Charged Disk?

What is the magnitude of electric field?

The magnitude of electric field is a measure of the strength of an electric field at a given point. It is usually expressed in units of Newtons per Coulomb (N/C) or Volts per meter (V/m).

How is the magnitude of electric field calculated?

The magnitude of electric field is calculated by dividing the electric force acting on a charge by the magnitude of the charge itself. It can also be calculated by dividing the potential difference by the distance between two points.

What factors affect the magnitude of electric field?

The magnitude of electric field is affected by the distance between two charges, the magnitude and sign of the charges, and the medium in which the charges are located. It is also affected by the presence of other charges in the vicinity.

How does the magnitude of electric field differ from electric potential?

Electric potential is a measure of the potential energy per unit charge at a given point in an electric field. It is a scalar quantity, whereas the magnitude of electric field is a vector quantity that represents the strength and direction of the electric field.

How does the magnitude of electric field relate to electric flux?

The magnitude of electric field is directly proportional to electric flux, which is a measure of the number of electric field lines passing through a given area. As the magnitude of electric field increases, so does the electric flux.

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