For the given diagram $E=\phi x N/C$, the net flux through the cube of side $x=1\, cm$, placed $x=1\, cm$ from the origin as shown is:
(E is acting towards positive x-axis and $\phi= 1$)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $1×10^{-6} Wb$
Net electric flux through a closed surface equals the difference in electric field across opposite faces multiplied by area
E = x (since φ = 1), direction → +x-axis
Cube side = 1 cm = 10⁻² m
Only the two faces perpendicular to x-axis contribute.
Other faces give zero flux because the field is parallel to them.
Left face: x = 1 cm = 1 × 10⁻² m
Right face: x = 2 cm = 2 × 10⁻² m
Electric field at faces
E₁ = 1 × 10⁻²
E₂ = 2 × 10⁻²
Area of each face
A = (1 cm)² = (10⁻²)² = 1 × 10⁻⁴ m²
Net flux
Flux enters from left face and exits from right face.
Φ = A (E₂ − E₁)
Φ = 1 × 10⁻⁴ × (2 × 10⁻² − 1 × 10⁻²)
Φ = 1 × 10⁻⁴ × 1 × 10⁻²
Φ = 1 × 10⁻⁶ Wb
Final Answer:
Φ = 1 × 10⁻⁶ Wb