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Question

Two charges \( 20 \, \mu\text{C} \) and \( -8 \, \mu\text{C} \) are placed 20 cm apart. What is the
potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2
\text{C}^{-2} \)).

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Explanation

**Sign of potential energy** indicates nature of interaction, like charges U>0, opposite U<0. Work done by field moving positive charge from higher to lower potential positive, as field does work W = q ΔV, ΔV negative when moving to lower V. U = (1/4 π ε₀) (q₁ q₂/r) = 9 × 10⁹ × (20 × 10⁻⁶ × (-8 × 10⁻⁶)/0.2) . U = 9 × 10⁹ × (-160 × 10⁻¹²/0.2) = -7.2 J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V = Q_total/C_total,

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