Electric Flux Through a 1x1x1 cm Box

[absolutezer0es]

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?

 

[Doc Al]

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.

 

[absolutezer0es]

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?

 

[Doc Al]

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.)

 

[absolutezer0es]

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?

 

[Doc Al]

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.

 

[absolutezer0es]

So what does the 150 mean? Does it have anything to do with the problem?

 

[Doc Al]

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.