The electric field in a certain region is defined by E = E₀ x l i . Determine the charge enclosed within a cubical volume defined by the planes x = 0 , x = a , y = 0 , y = a , z = 0 and z = a . Assume E₀ = 5 10^3 N C ⁻¹ , l = 2 cm , and a = 1 cm .

Step-by-step solution

The electric field is given by E = E₀ x l i . The flux through the cubical volume is non-zero only for the faces perpendicular to the x-axis, as the electric field has only an x-component. At the face x = 0 , the electric field is zero, so the flux ₁ = 0 . At the face x = a , the electric field is E = E₀ a l i . The area vector for this face is A = a^2 i . The flux through this face is ₂ = E A = E₀ a^3 l . The total electric flux through the cube is = ₁ + ₂ = E₀ a^3 l . According to Gauss's law, the total flux is r