Hello,
I have this number where I don't understand why there's a negative sign to it.
Consider a closed triangular box resting withing a horizontal electric field of magnitude E = 7.8 x 104 N/C as shown here. Calculate the electric flux through
(a) the vertical surface,
with all the measurements I get 1.8, but the answer is -1.8. Why is that? I mean the Electric Field is going through the rectangle and A should be in the same direction, because in the the next question they ask you about how much Flux goes through the slanted surface, and that one was positive.
on the surface, which way is negative, and which way is positive? Look at the coordinate system. Normally, on a box, outward is +, but that is not standard. If the E field is external, then on one vertical surface it will be going in (neg), and on the bottom, it will be +, going out.
this is the image
ww w.ux1.eiu.edu/~cfadd/1360/24Gauss/24Hmwk/24.05. html
I cant access it. Reread my explaination on + or - directions.
The flux is the dot product
Ô = (E,A) = E•A•cosα = =7.8•10^4•0.1•0.3•(-1) = - 2340 V•m.
α is the angle made by outward normal to the surface with the direction of the field lines. Here α = 180º, => cosα = -1
To understand why the answer for the flux through the vertical surface is negative, let's look at the concept of electric flux and how it is calculated.
Electric flux is a measure of the electric field passing through a given area. It is given by the equation:
Flux = Electric Field * Area * cos(θ)
where the Electric Field is the magnitude of the electric field, Area is the area vector perpendicular to the surface, and θ is the angle between the electric field and the normal to the surface.
In this case, the electric field is given as E = 7.8 x 10^4 N/C. To calculate the electric flux through the vertical surface, we need to determine the area vector and the angle θ.
For the vertical surface, the area vector is pointing in the positive y-direction (upwards). However, the electric field is pointing in the positive x-direction (to the right). The angle between these two vectors is 90 degrees (perpendicular to each other).
Now, let's calculate the flux using the formula:
Flux = Electric Field * Area * cos(θ)
Flux = (7.8 x 10^4) * (1.8 * 1.8) * cos(90)
If you calculate this expression, you will find that the flux through the vertical surface is -1.8 x 10^5 Nm^2/C. The negative sign indicates that the flux is directed opposite to the positive direction of the area vector. In other words, the electric field lines are entering the surface rather than leaving it.
The positive flux you mentioned for the slanted surface indicates that the electric field lines are leaving the surface, which is why it is positive.
So, in summary, the negative sign in the flux through the vertical surface indicates the direction of the electric field lines entering the surface, while the positive sign for the slanted surface indicates the direction of the electric field lines leaving the surface.