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 is ______. [Dimensions of cuboid = 1 × 2 × 3 m³] Image
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

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 is ______. [Dimensions of cuboid = 1 × 2 × 3 m³] Image

Physics · Circular Motion

JEE Mains 30 January 2023 Shift 2 Evening Shift

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.