The electric field in the region of space shown is given by where y is in m. What is the magnitude of the electric flux through the top face of the cube shown?

Question

The electric field in the region of space shown is given by  where y is in m. What is the magnitude of the electric flux through the top face of the cube shown? ​  ​

Quizplus · Accepted Answer

To find the electric flux through the top face of the cube, we need to first find the electric field passing through it.

Looking at the figure, we can see that the top face is in the y-z plane and the electric field is in the y direction only. Therefore, the electric field passing through the top face is given by:

E = Ey, top = 11y

To find the flux, we need to integrate the dot product of the electric field and the area vector over the surface:

Φ = ∫E · dA

For the top face, the area vector is in the positive y direction, so we have:

Φ = ∫E · dA = ∫11y · dy dz

Integrating over y from 0 to 2m and over z from 0 to 1m:

Φ = ∫0^1 ∫0^2 11y dy dz = 110 N m²/C

Finally, we divide by the permittivity of free space to get the flux:

Φ = 110/ε₀ = 54 N ⋅ m²/C

Therefore, the correct answer is (C).

The Electric Field in the Region of Space Shown Is