A hollow cylindrical box of length 1 m and area of cross-section 25 cm² is placed in a three-dimensional coordinate system. The electric field in the region is given by →E=50x^i, where E is in NC⁻¹ and x is in meters. Find (i) Net flux through the cylinder. (ii) Charge enclosed by the cylinder.

Area of the cross-section of the cylinder A=25×10⁻⁴ m²
Electric field at the face nearer to the origin E₁=50×0.5=25 N/C
Thus flux entering through this face φ₁=E₁A=25×25×10⁻⁴=6.25×10⁻² Wb
Distance of second face from origin =1+0.5=1.5 m
Electric field at the face away from the origin E₂=50×(1.5)=75 N/C
Thus flux leaving out through this face φ₂=E₂A=75×25×10⁻⁴=1.875×10⁻¹ Wb
(i) : Net flux through the cylinder φ=(1.875×10⁻¹-6.25×10⁻²)=1.25×10⁻¹ Wb
(ii) : Charge enclosed in the cylinder Q=φϵ₀
∴Q=1.25×10⁻¹×8.85×10⁻¹²=1.106×10⁻¹² C