A square of side a lies in the xy-plane with two of its sides along the coordinate axes. The electric field is $\vec{E}$ = E₀ $x$ $\hat{k}$ . Find the electric flux through the square.
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Question

A square of side a lies in the xy-plane with two of its sides along the coordinate axes. The electric field is E ⃗ \vec{E} E = E₀ x x x k ^ \hat{k} k ^ . Find the electric flux through the square.

G1 Physics · Accepted Answer

The area vector of the square is along 𝐤, so dΦ = 𝐄·d𝐀 = E₀x dA. Over the square, 0 ≤ x ≤ a and 0 ≤ y ≤ a. Thus Φ = E₀∫₀ᵃ∫₀ᵃ x dy dx = E₀a[a²/2] = E₀a³/2. Correct answer: B.