Electric field of a charged disc with a small circle cut out of it

[kirito]

Homework Statement

A very small circular area with radius A is cut out from a thin charged disk with total radius R, where A≪R. The remaining disk, which is centered at the origin, has a uniform surface charge density σ. The goal is to calculate the electric field at a point on the z-axis, at a distance z from the center of the disk.

Relevant Equations

gauss

I am having a bit of a problem understanding what to visualise since in the first part we found the electric field resultant from the disc shell The goal is to calculate the electric field at a point on the z-axis, at a distance z from the center of the disk.

now after they cut of the circle

but I am failing to understand the question ,is not the shell hallow if they are removing a disc where are they removing it from
I tried to read the solution yet I don't understand the question ,if a visualisation can be provided I am thankful

 

[kuruman]

The "relevant" equation that you show is not relevant here. There is no shell. See here for the relevant equation. You want the electric field on the axis of symmetry at some distance from the center of the disk.

The disk with the hole at its center has the same field on the axis as a whole disk with charge density $\sigma$ plus the field from a second concentric disk of same size of the hole that has negative charge density $-\sigma.$

 

[renormalize]

if a visualisation can be provided I am thankful

I'm unclear how this problem involves a "shell". To my understanding, the configuration described looks like this:

except that in the problem, the hole in the second disk is much smaller in diameter than in this illustration.
(Illustration is from here.)

 

[kirito]

I'm unclear how this problem involves a "shell". To my understanding, the configuration described looks like this:
View attachment 352160
except that in the problem, the hole in the second disk is much smaller in diameter than in this illustration.
(Illustration is from here.)

first and for most thanks to everyone for the quick replies , I think as everyone stated imagining something like this would do the trick and solving using superposition instead of integration would be wiser ,
the thing is though I am learning the course in a language thats not my native one , but the term they used in part one of the question was a thin spherical shell


and the solution for part 1 did indeed align with the term
then they demanded to use the result of section A
and used the spherical shell term so I could not imagine what the problem intitles
they even used a bit of a different approach for the same section and wrote in English electric field of a sphere and a disk and used them

 

[kirito]

I think I am starting to understand what they meant thanks to all of you
it seems like they did indeed consider a spherical shell but with a small hollow disk removed
and gave me a radius a<<R so I can use an approximation to solve the integral or use superposition
and assumed with such approximation the disk field should be similar to an infinite charged plane field

 

[kuruman]

first and for most thanks to everyone for the quick replies , I think as everyone stated imagining something like this would do the trick and solving using superposition instead of integration would be wiser ,
the thing is though I am learning the course in a language thats not my native one , but the term they used in part one of the question was a thin spherical shell

View attachment 352162
and the solution for part 1 did indeed align with the term
then they demanded to use the result of section A
and used the spherical shell term so I could not imagine what the problem intitles
they even used a bit of a different approach for the same section and wrote in English electric field of a sphere and a disk and used them

For future reference: Please do not post only part of a problem. If there are other parts, we need to know what they are in order to put the question into perspective. You can still solve the shell problem by using the superposition of the field from a charge shell without a hole and a "hole" with negative surface charge density placed on the surface of the shell.

 

[Vanadium 50]

The "relevant" equation that you show is not relevant here.

Nor is it an equation.

I agree with you, posting fragments of the problem, the equations and the attempt is not the path to success.

 

[kirito]

Nor is it an equation.

I agree with you, posting fragments of the problem, the equations and the attempt is not the path to success.

could you elaborate on what should one do to gain knowledge "path to success ", Any advice on what one should include in a post in general would help , I did read the guidelines, but I’m still getting used to the format of such sites.

I usually do not include the whole problem fearing that the post would be overly long with the attempts and the step by step thought process since I tried once and got feedback that even though including my thought process and whole solution or question can reveal what I do not understand yet it won't be helpful for the general public and would take too much time and effort to read and easy to forget what I am asking .

I seem to fail at understanding what is vital for a clear post and what can be omitted ,I will try to view posts with positive reviews and learn from them.

so if there are any attentional insight on how to fix the problems pointed out I am more than pleased to hear .

 

[Vanadium 50]

It's real simple. Look at the Forum Rules and follow them.

 

[berkeman]

Any advice on what one should include in a post in general would help , I did read the guidelines, but I’m still getting used to the format of such sites.

I usually do not include the whole problem fearing that the post would be overly long with the attempts and the step by step thought process since I tried once and got feedback that even though including my thought process and whole solution or question can reveal what I do not understand yet it won't be helpful for the general public and would take too much time and effort to read and easy to forget what I am asking .

I seem to fail at understanding what is vital for a clear post and what can be omitted ,I will try to view posts with positive reviews and learn from them.

so if there are any attentional insight on how to fix the problems pointed out I am more than pleased to hear .

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