Electric Flux Theory & Superposition | Find Electric Field at P

[maiad]

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.

 

[Doc Al]

Is it because the electric field through the surface is not uniform?

Exactly.

 

[maiad]

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?

 

[Doc Al]

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.

 

[sardar]

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.