27: Problem 27.4

INTRO:
The electric field is constant over each face of the cube shown in the figure (Figure 1)

Figure 1

PART A:
Does the box contain positive charge, negative charge, or no charge?

SOLUTION:

Φ_E = ∫E⋅dA

∫E = E_IN - E_OUT​

Let A be arbitrary area. Field is cube so surface area of any side is equal to surface area of any other side.

Let C be hypothetical charge inside cube

Φ_E = ∫E⋅dA = 0:

0 = C + [(15 - 20)_x + (15 - 10)_y + (15 - 20)_z]⋅A

→ C = 5 N/C          ∴ Positive charge​