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Practice question

MCQ

Question

Four charges \( +q, -q, +q, -q \) are at the corners of a square of side \( 2 \, \text{m} \) in order.
What is the potential at the center? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \,
\text{Nm}^2 \text{C}^{-2} \), \( q = 1 \, \mu\text{C} \)).

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Explanation

**Electric potential** V = k Q/r, k = 1/(4π ε₀)=9×10⁹ N·m²/C², Q charge (C), r distance (m), scalar, potential at surface of spherical conductor radius R, V = k Q/R. Potential difference ΔV = V_B - V_A = -∫ E·dl, work per unit charge to move charge without acceleration. Distance from center to each corner = √(2) m . V = 9 × 10⁹ ( (1 × 10⁻⁶/√(2)) + (-1 × 10⁻⁶/√(2)) + (1 × 10⁻⁶/√(2)) + (-1 × 10⁻⁶/√(2)) ) = 0 V . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel,

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