The electric field in the region of space shown is given by N/C where y is in m. What is the magnitude of the electric flux through the top face of the cube shown? A) 90 N ⋅ m²/C B) 6.0 N ⋅ m²/C C) 54 N ⋅ m²/C D) 12 N ⋅ m²/C E) 126 N ⋅ m²/C

Question

Quizplus · Accepted Answer

To find the electric flux through the top face of the cube, we need to integrate the electric field over that face:
Φ = ∫E⋅dA
Since the electric field is given by E = 11y N/C, and the top face is a square of side length 0.1 m (according to the diagram), the area element dA is also a square of side length 0.1 m, and is perpendicular to the electric field. Therefore, we have:
Φ = ∫E⋅dA = ∫(11y)(0.1²) dy
Φ = (0.11 N/C)(0.1²/2)(1.8 - 1.2) = 0.054 N⋅m²/C
Therefore, the correct answer is C, 54 N⋅m²/C.

The Electric Field in the Region of Space Shown Is