# How can we solve the infinite sheet problem for electric field at a point P?

• latentcorpse
In summary, the conversation discusses finding the electric field for an infinitely large flat sheet of material. The formula for the electric field is given, and it is suggested to use a ring method of integration to solve the problem. The question of how to find the total charge is brought up and it is confirmed that it can be found by using an integral from 0 to infinity. The process of finding the electric field from all the infinitesimal rings is also mentioned.
latentcorpse
http://www.ph.ed.ac.uk/teaching/course-notes/documents/76/1000-Jun2001.PDF

in q5, the second part of the question. How do we even start to do this? (it's the bit about finding the field if you assume that it's part of an infinitely large flat sheet of material)

my field from the first part of the question is

$E(P)=\frac{1}{4 \pi \epsilon_0} \frac{qd}{a}$

since $dE_z=\frac{dq}{4 \pi \epsilon_0}{\vec{a} \cdot \vec{\hat{z}}}{a^3}=\frac{1}{4 \pi \epsilon_0} \frac{dq a \cos{\theta}}{a^3}$ then i canceled the a's and subbed $\cos{\theta}=\frac{d}{a}$

I believe that problem concerning the infinite sheet means using a ring method of integration.

Each ring has charge C*2πr dr, and each ring contributes to the E-field at P.

For an infinite sheet, 0 < r < ∞

im a bit confused - does that mean i get the total charge by $\int_0^{\infty} C 2 \pi r dr$?

Yes, but one wishes to find E(P), so one must dE from all the infinitesimal rings for 0 to ∞. Note that as r -> ∞, the angle from the vertical axis to the line from P to the ring of charge.

## Question 1: What is the "Infinite sheet problem" in science?

The "Infinite sheet problem" is a theoretical problem in physics that involves calculating the gravitational field produced by an infinite sheet of matter with uniform density. It is often used as a simplified model to study the behavior of gravity in certain systems.

## Question 2: How is the gravitational field of an infinite sheet of matter calculated?

The gravitational field of an infinite sheet of matter is calculated using the formula Gσ, where G is the gravitational constant and σ is the surface density of the sheet. This formula assumes that the sheet is infinite in size and has a uniform density.

## Question 3: What are the assumptions made in the "Infinite sheet problem"?

The "Infinite sheet problem" makes several assumptions, including that the sheet is infinite in size, has a uniform density, and is perfectly flat. It also assumes that the sheet is infinitely thin and that gravity acts in a straight line at all points on the sheet.

## Question 4: How is the "Infinite sheet problem" used in real-world applications?

The "Infinite sheet problem" is often used as a simplified model to study the behavior of gravity in certain systems, such as the gravitational field around a planet or galaxy. It is also used in theoretical physics to study the properties of infinite systems.

## Question 5: What are some limitations of the "Infinite sheet problem"?

The "Infinite sheet problem" is a simplified model that does not accurately represent real-world situations. It does not take into account the effects of curvature and rotation, and it assumes that the sheet has an infinite size, which is not possible in reality. Additionally, the problem becomes more complex when the sheet is not perfectly flat or has a non-uniform density.

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