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Practice question

MCQ

Question

An electric dipole with moment \( p = 4 \times 10^{-9} \, \text{C m} \) lies along the x-axis. What is
the potential at \( (-2, 0, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \,
\text{Nm}^2 \text{C}^{-2} \)).

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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. Along the dipole axis ( θ = 180° ): V = -(1/4 π ε₀) (p/r²) . V = -9 × 10⁹ × (4 × 10⁻⁹/2²) = -9 × 10⁹ × (4 × 10⁻⁹/4) = -9 V . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC

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