Electrostatic Potential and Capacitance

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Electrostatic potential (V) at a point is the work done per unit positive charge by an external force in bringing a test charge from infinity to that point. Only potential difference is physically sig…

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Given: Q = 5 × 10⁻⁶ C, r = 20 cm = 0.20 m, k = 9 × 10⁹ N·m²/C² Formula: V = kQ/r Step 1: Substitute values V = (9 × 10⁹ N·m²/C²) × (5 × 10⁻⁶ C) / (0.20 m) Step 2: Calculate numerator Numerator = 9 …

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Inside a conductor, free charge carriers (electrons in metals) continuously move until the internal electric field becomes zero. If any field existed, charges would experience a force and continue mov…

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Given: q₁ = +3 × 10⁻⁸ C, q₂ = -2 × 10⁻⁸ C, separation = 15 cm = 0.15 m Let point P be at distance x from q₁, where potential = 0 Formula: V_total = kq₁/x + kq₂/(0.15-x) = 0 Step 1: Set up equation …

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Formula: U = (1/4πε₀) × (q₁q₂/r₁₂) = kq₁q₂/r₁₂ Where: - q₁, q₂ are the charges - r₁₂ is the distance between them - k = 9 × 10⁹ N·m²/C² (Coulomb's constant) - ε₀ = 8.85 × 10⁻¹² C²/(N·m²) Unit: Joule…

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Mechanism of Capacitance Increase: 1. Polarization: The dielectric molecules (polar or non-polar) align or deform in the external electric field - Polar molecules: Dipoles rotate to align with fie…

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Given: A = 100 cm² = 100 × 10⁻⁴ m² = 10⁻² m², d = 2 mm = 2 × 10⁻³ m, ε₀ = 8.85 × 10⁻¹² F/m Formula: C = ε₀A/d Step 1: Identify the values with correct units A = 10⁻² m² d = 2 × 10⁻³ m ε₀ = 8.85 × 10…

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Mathematical Relationship: E = -dV/dr (in one dimension) E = -∇V (in three dimensions, gradient) Physical Meaning: 1. Magnitude: |E| = -ΔV/Δl - Electric field equals the negative rate of change of…