Electrostatic Potential and Capacitance

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Electrostatic potential energy is the energy stored in a charge due to its position in an electric field. It equals the work done by an external force in bringing the charge from infinity to that poin…

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Electrostatic potential (V) at a point is the work done per unit positive charge in bringing a test charge from infinity to that point. V = W/q. SI unit is volt (V), where 1 volt = 1 joule/coulomb. No…

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V(r) = (1/4πε₀) × (Q/r), where V(r) is potential at distance r from point charge Q, ε₀ is permittivity of free space (8.85 × 10⁻¹² C²N⁻¹m⁻²), and r is distance from charge. For Q > 0, V > 0; for Q < 0…

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For an electric dipole: V = (1/4πε₀) × (p cos θ/r²) = (1/4πε₀) × (p⃗·r̂/r²), where p is dipole moment, θ is angle between p⃗ and position vector, r is distance. Key points: (1) Varies as 1/r² (not 1/r…

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The total electrostatic potential at any point due to a system of charges is the algebraic sum of potentials due to individual charges. V = V₁ + V₂ + ... + Vₙ = (1/4πε₀) Σ(qᵢ/rᵢₚ), where rᵢₚ is distan…

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Equipotential surfaces are surfaces where potential has the same constant value at all points. Properties: (1) Electric field is always perpendicular to equipotential surface, (2) No work is done in m…

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Electric field points in direction of steepest decrease of potential. |E| = -dV/dl, where dl is perpendicular distance between equipotential surfaces. In one dimension: E = -dV/dx. The negative sign i…

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U = (1/4πε₀) × (q₁q₂/r₁₂), where q₁, q₂ are the charges and r₁₂ is distance between them. If q₁q₂ > 0 (like charges): U > 0 (repulsive, positive work needed). If q₁q₂ < 0 (unlike charges): U < 0 (attr…