A cube of side 0.5 m is placed in a non-uniform electric field E = 150 y² j (N/C), oriented so that the relevant faces are perpendicular to the y-axis as shown. Find the net charge enclosed within the cube.

3.8 * 10⁻¹¹ C
8.3 * 10⁻¹¹ C
3.8 * 10⁻¹² C
8.3 * 10⁻¹² C

Correct answer: 8.3 * 10⁻¹² C

Solution

The field points along +y and varies as y². Flux through the bottom (y=0) face is zero, and through the top (y=a) face is E(a)*a². With a = 0.5 m, E(a) = 150*(0.5)² = 37.5 N/C, area = 0.25 m², so flux = 9.375 N m²/C. Then q = epsilon0 * flux about 8.3 * 10⁻¹² C.

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