Magnitude of the flux through a rectangle

[guyvsdcsniper]

Homework Statement

A 2.0 cm × 3.5 cm rectangle lies in the xz-plane.
What is the magnitude of the electric flux through the rectangle if E⃗ =(150ı^−240k^)N/C?
What is the magnitude of the electric flux through the rectangle if E⃗ =(150ı^−240ȷ^)N/C?

Relevant Equations

E.F. = E*A

I have attached the work to this problem and although it has different parameters than what I have listed in my post the basis to solving the problem is the same.

I am confused on why this rectangle in this problem is considered to b in the j unit vector direction. Is it because its face will face the j axis?

 

[haruspex]

Homework Statement:: A 2.0 cm × 3.5 cm rectangle lies in the xz-plane.
What is the magnitude of the electric flux through the rectangle if E⃗ =(150ı^−240k^)N/C?
What is the magnitude of the electric flux through the rectangle if E⃗ =(150ı^−240ȷ^)N/C?
Relevant Equations:: E.F. = E*A

I have attached the work to this problem and although it has different parameters than what I have listed in my post the basis to solving the problem is the same.

I am confused on why this rectangle in this problem is considered to b in the j unit vector direction. Is it because its face will face the j axis?

The vector representing an area element is normal to the element, yes. If it is part of a surface enclosing a volume of interest then it point out of the volume.
Note that if the area element $\vec {dS}$ is translated along a vector element $\vec {dr}$ then the volume swept out is the dot product.

 

[guyvsdcsniper]

The vector representing an area element is normal to the element, yes. If it is part of a surface enclosing a volume of interest then it point out of the volume.
Note that if the area element $\vec {dS}$ is translated along a vector element $\vec {dr}$ then the volume swept out is the dot product.

So I know that If I dot product to different unit vectors I get 0, hence the part of the homework question I posted is 0.

The second part of the question, the electric field has a J component so I was able to multiply the area by the unit vector. My answer came out to be .168 N/C which is correct.

But I was wondering why do we omit the negative in the electric fields J component?

 

[kuruman]

But I was wondering why do we omit the negative in the electric fields J component?

Because a rectangle is a surface that encloses no volume, therefore the "outward normal" cannot be defined. In such cases, one takes the positive value for the flux by convention.