Gaussian surface - which charges contribute to the electric field

[alex21]

Homework Statement

in the following figure, the dashed line denotes a Gaussian surface
enclosing part of a distribution of four positive charges.

a) which charges contribute to the electric field at P?
b) is the value of the flux though the surface, calculated using
only the electric field due to q1 and q2, greater than, equal to,
or less than that obtained using the field due to all four charges?

Homework Equations

&Phi;=&int;E*A=Q<sub>enclosed/&epsilon;
Φ=∫E*A=Qenclosed/ε

The Attempt at a Solution

a)what I tried to do is to draw the field line of each charge since all of them are positive they will repel each other and at P the electric field will be zero so none of them contributes to the field
b) I don't fully understan question B but I would say that since all charges are equal and for the flux through the surface I will only consider q1 and q2 the flux must be equal

hel please!

 

[member 392791]

I think you should review a gaussian surface and how the electric field and charges contained within relate. Your equation for the flux should be enough to let you know. The subscript for Q_enclosed is precisely that, the charge enclosed in the gaussian surface. Also, this question belongs in the introductory physics homework subforum, not engineering.

 

[alex21]

ok second chance I was wrong about a) I can say now that all of them contribute to field at P because
The electric fiedl in the expression for Gauss´s law refers to the total electric field, not just the electric field due to any enclosed charge.
about question b) the charge enclosed in gaussian surface is q1+q2, if we use the field due to all four charges then the charge enclosed will be q1+q2+q3+q4 therefore the flux through the surface using only q1 and q2 it would be less if we use all four charges.

 

[alex21]

:( no body help me with me question though

 

[rezeew]

I would like to clarify and expand upon the response to this content.

Firstly, a Gaussian surface is a hypothetical surface that is used to simplify calculations of electric fields. It is an imaginary surface that is chosen to enclose a specific region of space, and it is often chosen to be a symmetrical shape (such as a sphere or a cylinder) to simplify calculations.

In this scenario, the dashed line represents the Gaussian surface enclosing part of a distribution of four positive charges. The question asks which charges contribute to the electric field at point P, which is located outside of the Gaussian surface. To answer this question, we need to consider the electric field due to each individual charge at point P.

As mentioned, all four charges are positive and will therefore repel each other. At point P, the electric field will be a combination of the electric fields due to each individual charge. However, since the charges are symmetrically arranged, the electric field due to each charge will cancel out and result in a net electric field of zero at point P. Therefore, none of the charges contribute to the electric field at point P.

Moving on to the second question, it asks whether the value of the flux through the surface, calculated using only the electric field due to q1 and q2, is greater than, equal to, or less than that obtained using the field due to all four charges. To answer this question, we need to understand the concept of flux.

Flux is a measure of the flow of a physical quantity through a given surface. In this case, we are interested in the flux of the electric field through the Gaussian surface. The electric field due to all four charges will result in a certain amount of flux through the surface. However, if we only consider the electric field due to q1 and q2, the resulting flux will be less since the electric field is weaker. This is because the electric field due to q3 and q4 also contribute to the total flux through the surface.

In conclusion, none of the charges contribute to the electric field at point P, and the flux through the surface will be less if we only consider the electric field due to q1 and q2 compared to considering the electric field due to all four charges. This demonstrates the importance of considering all contributing factors when calculating physical quantities in science.