Why is this flux negative and not postiive?

[mr_coffee]

Hello again. The first problem I even came close to getting right, and yet i still missed it by a negative sign. There is a square surface measures 3.2mm on each side. It is immersed in a uniform elelctric field with magnitude E = 1800 N/C and with field lines at an angle of 35 degrees with normal to surface, as shown. Take that normal to be directed "outward" as though the surface were one face of a box. Calculate the electric flux through the surface.

So I used Flux = E cos(35)A; Plugged and chugged and got Flux = .015 Nm^2/C. The answer in the back of the book is Flux = -.015 Nm^2/C. Why would it be negative? If u need the image tell me and i'll scan it. It looks like a top of a box. Normal is straight up from the boxes surface pointing to the sky. the elctrical field lines are going through the box South Westward, you know if u draw a heart and put an arrow through it, that's what the lines look like they are doing.

 

[Doc Al]

Careful when you "plug and chug". Remember that if the field points out of the surface (in the same direction as the normal) then the flux is positive; in this case the field points into the surface. Your formula would work if you used the angle that the field makes with the normal vector: that angle is 145 degrees, not 35 degrees. (Draw a picture.) It makes an angle of 35 degrees with the negative of the normal vector, which is 180 degrees away from the positive normal vector.

I recommend that you use the formula to get the magnitude of the flux but use a picture (and the rule I gave above) to find the sign of the flux.

 

[thepatientmental]

The reason why the flux is negative in this case is because of the direction of the electric field lines. In this scenario, the electric field lines are entering the surface at an angle of 35 degrees, which means they are not perpendicular to the surface. This results in a negative flux value because the electric field is not passing through the entire surface, but only a portion of it.

To understand this better, imagine the electric field lines as a stream of water and the surface as a screen. When the water hits the screen at an angle, it does not pass through the entire surface but only a portion of it. This results in a negative flow or flux because the water is not fully passing through the screen.

In the same way, the electric field lines passing through the surface at an angle results in a negative flux value because the field is not fully passing through the surface. This is why the answer in the book is negative.

I hope this helps clarify why the flux is negative in this scenario. Keep practicing and you will get the hang of it!