Calculate Flux in a closed Triangle

[RedPhoenix]

Homework Statement

Consider a closed triangular box resting within a horizontal electric field of magnitude E = 7.80 & 104 N/C as shown in Figure P24.4. Calculate the electric flux through (a) the vertical rectangular surface, (b) the slanted surface, and (c) the entire surface of the box.

Homework Equations

Flux = EAcos( )

The Attempt at a Solution

for a) I did

(7.8E4)(.1x.3)cos(0) = 2.34kN

The answer should be negative, why?
Would it be cos(180) instead? What is the reason for this?

for b), the slanted plane, the answer is 2.34kN, but why would it be? I did (7.8E4)(.1x.3)cos(0), which gives the right answer, but why is it 0? not 60 or something?

c) I am assuming because a and b cancel each other when added together.


A little input would be nice, thanks :)

Matt

 

[Donaldos]

a) The surface normal and the electric field point in opposite directions.

b) The area of the slanted surface is not $$0.1 \times 0.3$$ but $$\frac{0.1}{\cos 60} \times 0.3$$

$$\Phi_E=(7.8\times 10^4) \times \frac{0.1}{\cos 60} \times 0.3 \times \cos 60=(7.8\times 10^4) \times \0.1\times 0.3$$

 

[tomcue]

Hello Matt,

It's great to see you working through this problem and using the correct equations. Your analysis is mostly correct, but let me clarify a few things for you.

First, the reason why the answer for part (a) is negative is because the electric flux is a vector quantity and its direction is determined by the direction of the electric field and the orientation of the surface. In this case, the electric field is pointing to the right (positive x-direction) and the surface is perpendicular to it (angle of 0 degrees). Therefore, the flux is positive in the positive x-direction. However, since the surface is facing in the opposite direction of the electric field, the flux is actually negative. This is why we use cos(180) instead of cos(0) in this case.

For part (b), your answer of 2.34kN is correct. The reason why the angle is 0 degrees is because the slanted surface is parallel to the electric field, making the angle between them 0 degrees. Therefore, cos(0) = 1 and the flux is simply the product of the electric field and the area of the slanted surface.

For part (c), your reasoning is correct. The flux through the entire surface of the box is the sum of the flux through the vertical and slanted surfaces, which cancel each other out and give a net flux of 0.

I hope this helps clarify your understanding of electric flux. Keep up the good work!