Question 7

**Setting up:** For infinite sheets, the field in any region is E = (Σσ_left − Σσ_right) / (2ε₀), directed to the right (taking rightward positive). Also, σ₀/ε₀ = (9×10⁻⁶)/(9×10⁻¹²) = 10⁶ V/m, and with d = 1 μm, (σ₀/ε₀)·d = 1 V. **Configuration I** (+σ₀, −σ₀, +σ₀, −σ₀, +σ₀, −σ₀): - Region 1: left = +σ₀, right = −σ₀ → E = σ₀/ε₀ - Region 2: left = 0, right = 0 → E = 0 - Region 3: E = σ₀/ε₀ - Region 4: left = 0, right = 0 → E = 0 ✔ (A) correct - Region 5: E = σ₀/ε₀ Potential difference between first and last sheet = 3 × (σ₀/ε₀)·d = 3 V, not 5 V → (C) incorrect. **Configuration II** (+σ₀/2, −σ₀, +σ₀, −σ₀, +σ₀, −σ₀/2): - Region 1: left = σ₀/2, right = −σ₀/2 → E = σ₀/(2ε₀) - Region 2: left = −σ₀/2, right = +σ₀/2 → E = −σ₀/(2ε₀) - Region 3: left = +σ₀/2, right = −σ₀/2 → E = σ₀/(2ε₀), not σ₀/ε₀ → (B) incorrect - Region 4: E = −σ₀/(2ε₀) - Region 5: E = σ₀/(2ε₀) Potential difference between first and last sheet = (½ − ½ + ½ − ½ + ½)(σ₀/ε₀)d = 0.5 V ≠ 0 → (D) incorrect. Only (A) is correct.

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