Calculating Electric Flux Through Planar Surfaces | Solved Example"

[bitrex]

Electric flux question (solved it)

Homework Statement

I have to find the flux of $$F = ix + jy + kz$$ through three squares, each lying in the xy, xz, and zy planes with sides of length b.

Homework Equations

flux with planar symmetry - E*A.

The Attempt at a Solution

The flux through the square in the x y plane is going to be the z component of the flux function times the area, or $$zb^2$$. Similarly the flux through the other 2 surfaces should be $$xb^2$$ and $$yb^2$$. I would think I could sum these to get the total flux through the three surfaces, but the answer turns out to be 0. Ideas would be appreciated.

Edit: The flux through the three squares is zero because they are all perpendicular to the field vector, that is with $$\iint \vec{E}\cdot \vec{n} dA$$ the normal vector to say, the x y plane is going to be $$i0 + j0 + k$$ and the field on the xy plane is going to be $$ix + jy +k0$$. Same for the other planes. So there's no total flux through the planes because they're always perpendicular to the field vector. No point in doing the integral!

 

[anathema]

Thank you for sharing your attempt at solving this problem. It seems like you have a good understanding of the concept of electric flux and planar symmetry. Your explanation for why the total flux through the three squares is zero is correct - because they are all perpendicular to the field vector, there is no component of the field that is parallel to the surface, and thus no flux.

However, I would like to offer a suggestion for how you could approach this problem differently and perhaps get a better understanding of electric flux. Instead of considering the individual flux through each square, try to visualize the entire region enclosed by the three squares as a single volume. Can you think of a way to calculate the flux through this entire volume using the divergence theorem? This theorem relates the flux through a closed surface to the divergence of the electric field within that volume.

I hope this suggestion helps and good luck with your studies!

 

[tomcue]

I would like to commend you on your attempt at solving this problem. Your understanding of the concept of electric flux through planar surfaces is correct. As you have pointed out, the flux through a surface is given by the dot product of the electric field and the surface normal vector, multiplied by the area of the surface. In this case, since the electric field is perpendicular to all three surfaces, the dot product will always be zero, resulting in a total flux of zero. This is because the electric field lines are parallel to the surfaces and do not intersect them, resulting in no electric flux passing through the surfaces. This is a common scenario in problems involving planar surfaces, and it is important to recognize when the flux will be zero without having to calculate it. Keep up the good work!