Infinitesimal Electric field of slice of disk

In summary, the problem involves a disk of radius R with a uniform surface charge density σ. The goal is to calculate the infinitesimal electric field dE due to a circular slice of charge dQ on the disk, expressed in terms of σ, r, and R. The attempted solution involves using the equation for electric field, E = kQ/d^2, and finding the value of dQ, which is equal to 2πσr dr. After substituting for dQ and solving for dE, there is confusion over what distance to use, either x or r. The solution using x as the distance could not be expressed solely in terms of σ, r, and R. The problem also references using results from the
  • #1
j3dwards
32
0

Homework Statement


A disk of radius R carries a uniform surface charge density σ.

(a) Using the results for the uniformly charged ring given in the lectures, or otherwise, compute the infinitesimal electric field dE due to the circular slice the disk of charge dQ shown in the figure. Express the result in terms of σ, r and R.

Homework Equations


E=kQ/d2

The Attempt at a Solution


qEx=kdQ/r2

dQ=σdA=2πσr dr

dr=R-r

dEx=σ(R-r)/2rεo

I'm not sure whether to put the distance d as x or just use the origin so just use r?

But when I used x as the distance, i couldn't put the answer in terms of σ, r and R. My workings for the use of x as the distance were:

dEx=k2πσxr/(r2+x2)3/2
 
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  • #3
rude man said:
" ... shown in the figure. ..."??
 

Attachments

  • electrodynamicsfig1.png
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  • #4
"Using the results for the uniformly charged ring given in the lectures, ... "
Are you doing this? What did they give you?
 

Related to Infinitesimal Electric field of slice of disk

1. What is an infinitesimal electric field?

An infinitesimal electric field is a very small, localized electric field that exists at a specific point in space. It is usually represented by the symbol dE and is used in calculus to calculate the total electric field at a particular point.

2. How is the infinitesimal electric field of a slice of disk calculated?

The infinitesimal electric field of a slice of disk can be calculated using the formula dE = k * dq * r / r^3, where k is the Coulomb's constant, dq is the charge element of the disk, and r is the distance from the charge element to the point where the electric field is being measured.

3. What is the significance of studying the infinitesimal electric field of a slice of disk?

Studying the infinitesimal electric field of a slice of disk allows us to understand the behavior of electric fields in more complex systems. It also helps in calculating the total electric field at any point due to multiple charges or a continuous charge distribution.

4. How does the infinitesimal electric field of a slice of disk affect the overall electric field of a larger system?

The infinitesimal electric field of a slice of disk contributes to the overall electric field of a larger system by adding up with the electric fields of other elements in the system. This allows us to use the superposition principle to calculate the total electric field at any point in the system.

5. Can the infinitesimal electric field of a slice of disk be negative?

Yes, the infinitesimal electric field of a slice of disk can be negative. This indicates that the electric field is pointing in the opposite direction of the chosen coordinate system. In other words, the electric field is directed towards the disk rather than away from it.

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