As shown in figure, a cuboid lies in a region with electric field E = 2x²î - 4yĵ + 6k̂ N C⁻¹. The magnitude of charge within the cuboid is nε₀ C. The value of n i $s ______.$ [Dimensions of cuboid = 1 × 2 × 3 m³]

Question

G1 Physics · Accepted Answer

Using Gauss's law, net flux is sum through opposite faces. For x faces, ΔE(x)=2(1²)-0=2 and area=2×3=6, giving +12. For y faces, ΔE(y)=-4(2)-0=-8 and area=1×3=3, giving -24. z-component is constant, so net z flux is zero. Net flux = -12, so |q|=12ε₀. Hence n=12.

As shown in figure, a cuboid lies in a region with electric field E = 2x²î - 4yĵ + 6k̂ N C⁻¹. The magnitude of charge within the cuboid is nε₀ C. The value of n i s ______. [Dimensions of cuboid = 1 × 2 × 3 m³]