Electric Flux Through a 1x1x1 cm Box

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Homework Help Overview

The problem involves calculating the net electric flux through a 1x1x1 cm box situated in a specified electric field, described by the equation E = (350x + 150)i N/C, where x is in meters. Participants are exploring the implications of the electric field's dependence on the position within the box.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of electric flux using the provided formula and question the validity of simply multiplying by two for the front and back sides of the box. There is confusion regarding the interpretation of the electric field expression and its implications at different positions within the box.

Discussion Status

There is an ongoing exploration of the electric field's behavior at specific points, with some participants questioning the assumptions made about the uniformity of the field across the box. Guidance has been offered regarding the need to calculate the flux through each face of the box separately, and the significance of the constant term in the electric field expression is being clarified.

Contextual Notes

Participants are grappling with the implications of the electric field's dependence on the x-coordinate and how this affects the calculation of flux through the box's surfaces. There is also a reference to a textbook answer that may not align with the current calculations being discussed.

absolutezer0es
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Homework Statement



A 1x1x1 cm box with edges aligned in the xyz-axes is in the electric field E = (350x + 150)i N/C, where x is in meters. What is the net electric flux through the box?

Homework Equations



flux = ExAx + EyAy + EzAz

The Attempt at a Solution



I substituted into the formula above, including 0.01m for x. I get:

flux = [(350*0.01 + 150)(0.01)^2] + 0 + 0 = 0.01535 Nm^2/C

I then multiply by two because the field is coming through the back and front of the box. I'm not getting the answer right though. What am I missing?
 
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absolutezer0es said:
I then multiply by two because the field is coming through the back and front of the box.
You cannot just multiply by 2. Calculate the flux through the front and back sides. (They aren't the same.) Then add to get the net flux, being careful with signs.
 
Why aren't they the same? Isn't it a cube? Maybe I don't understand the expression (350x + 150)i like I think I do.

Does the expression mean 350x on the way in and 150 on the way out?
 
absolutezer0es said:
Maybe I don't understand the expression (350x + 150)i like I think I do.
What's the field at x = 0? (Where one side is.) At x = 0.01? (Where the other side is.)
 
I'm still lost. The field at x=0? There are an infinite number of points on x=0, depending on y and z, no? Same at x=0.01.

I mean, the answer is 3.5x10^-4, according to my text. I substituted 0.01m into the expression and multiplied by (0.01)^2. Don't have a clue why though. What happened to the 150?
 
absolutezer0es said:
The field at x=0? There are an infinite number of points on x=0, depending on y and z, no? Same at x=0.01.
The field only depends on x. So all points with the same x value have the same field.
 
So what does the 150 mean? Does it have anything to do with the problem?
 
absolutezer0es said:
So what does the 150 mean? Does it have anything to do with the problem?
Of course it does! 350x + 150 is a function that gives you the magnitude of the electric field at any point. You can't leave out the 150.
 

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