# Electric Flux Theory & Superposition | Find Electric Field at P

In summary, the conversation discusses finding the electric field at point P using the equation \Phi=\intE dA=Qenclosed/\epsilon. However, this method was found to be incorrect due to the electric field not being uniform. The correct method, using superposition, was later used to get the right answer. The discussion also touched upon the concept of electric field and flux changing when point charges are shifted within a Gaussian space. It is noted that only in cases of sufficient symmetry will the electric field be uniform.
https://www.smartphysics.com/Content/Media/Images/EM/03/h3_lineD.png

In the image above, i was asked to find the electric field at point P. since the y-components cancel due to symmetry, i used he equation $\Phi$=$\int$E dA=Qenclosed/$\epsilon$ .

I found q1 and q2 by multiplying (charge density x h). then from that, i added the charges up to get Q(enclosed). I found my E by $\Phi$/(2πah).
This method was wrong apparently but i don't know why. can someone explain?
Is it because the electric field through the surface is not uniform?

I later used superposition instead and i got the right answer.

Last edited by a moderator:
Is it because the electric field through the surface is not uniform?
Exactly.

There were also examples of point charges spread abritraily in a guassin space. Would that not be uniformed also? I would think that the electric flux should not change if the points charges shifted withing the guassin space, but the electric field should also change when the point charges move. Is my assumption correct?

There were also examples of point charges spread abritraily in a guassin space. Would that not be uniformed also?
No reason to think that an arbitrary distribution of charges within a Gaussian surface would produce a uniform field at the surface. Only in cases of sufficient symmetry would the the field be uniform.
I would think that the electric flux should not change if the points charges shifted withing the guassin space, but the electric field should also change when the point charges move. Is my assumption correct?
Yes, you are correct.

I would like to address the issue of finding the electric field at point P using electric flux theory and superposition. The electric flux theory states that the electric field passing through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the medium. This method can be used to find the electric field at point P in the given scenario.

However, it seems that the method used by the individual in the image is incorrect. The electric field through the surface is not uniform due to the presence of two point charges, q1 and q2, and thus cannot be calculated using the formula \Phi/(2πah). This is because the electric field is a vector quantity and its magnitude and direction vary at different points in space.

Instead, the correct approach would be to use superposition, which states that the total electric field at a point due to multiple charges is equal to the vector sum of the individual electric fields at that point. By using this method, one can break down the problem into simpler components and calculate the electric field at point P due to each individual charge. Then, by taking the vector sum of these individual electric fields, the total electric field at point P can be determined.

In conclusion, while the electric flux theory is a valid approach to finding the electric field at a point, it is important to consider the non-uniformity of the electric field in certain scenarios. In such cases, the method of superposition is a more appropriate approach to accurately calculate the electric field at a given point.

## 1. What is electric flux theory?

Electric flux theory is a concept in electromagnetism that describes the flow of electric field lines through a given surface. It is a measure of the strength of an electric field passing through a specific area and is represented by the symbol ΦE.

## 2. How is electric flux calculated?

Electric flux is calculated by taking the dot product of the electric field vector and the surface area vector. This can be represented mathematically as ΦE = E⃗ ⋅ A⃗, where E⃗ is the electric field vector and A⃗ is the surface area vector.

## 3. What is superposition in electric flux theory?

Superposition is a principle in electric flux theory that states that the total electric flux through a surface is equal to the sum of the individual electric fluxes from each source that contributes to the field.

## 4. How can I find the electric field at a specific point using electric flux theory?

To find the electric field at a specific point, you can use the superposition principle to calculate the electric field contributions from each source and then add them together to get the total electric field at that point. Alternatively, you can use Gauss's law, which relates the electric flux through a closed surface to the enclosed charge and the permittivity of the medium.

## 5. Can electric flux theory be applied to non-uniform electric fields?

Yes, electric flux theory can be applied to both uniform and non-uniform electric fields. However, the calculations may be more complex for non-uniform fields as the electric field and surface area vectors may vary at different points on the surface.

Replies
25
Views
2K
Replies
30
Views
2K
Replies
5
Views
1K
Replies
14
Views
1K
Replies
2
Views
2K
Replies
1
Views
4K
Replies
35
Views
3K
Replies
3
Views
936
Replies
2
Views
4K
Replies
8
Views
3K