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Question

A dipole \( p = 10 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \(
90^\circ \) in a field \( E = 4 \times 10^5 \, \text{N/C} \). What is the work done?

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Explanation

**Electrostatic shielding** inside hollow conducting shell field zero when no charges inside, regardless of external field, because free charges redistribute on outer surface to cancel external field inside conductor, E=0 inside material in equilibrium, consequence of Gauss's law and conductor property. Work done: W = p E (cos θ₀ - cos θ₁) = 10 × 10⁻⁹ × 4 × 10⁵ × (cos 0° - cos 90°) . W = 10 × 10⁻⁹ × 4 × 10⁵ × (1 - 0) = 4 × 10⁻³ J . 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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