Electric Potential and Capacitors

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Electric Potential at a point is defined as the work done against the electric force in moving a unit positive charge from infinity (outside the field) to that point. Formula: V = W / q₀ Key Points:…

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Given: • Work done W = 4 × 10⁻⁵ J • Charge q₀ = 2 × 10⁻⁶ C Formula: V_AB = W_AB / q₀ Step 1: Substitute values V_AB = (4 × 10⁻⁵ J) / (2 × 10⁻⁶ C) Step 2: Calculate V_AB = 4/2 × 10⁻⁵⁺⁶ = 2 × 10¹ = 2…

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Setup: Point charge +q at O, point P at distance r from O. Derivation Steps: Step 1: Electric field at distance x from +q: E = (1/4πε₀) × (q/x²) Step 2: Work done in moving test charge q₀ from ∞ to…

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Given: • V = 400 V • E = 150 N/C Find: x and q Step 1: Use relation E = V/x (for point charge, valid near the charge) 150 = 400 / x x = 400/150 = 2.67 m Step 2: Use E = (1/4πε₀) × (q/x²) 150 = (9 ×…

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Dipole: charges −q at A and +q at B, separated by 2l, dipole moment p = q × 2l. General Formula: V = p cosθ / (4πε₀r²) Special Cases: 1. Axial line (side of +q), θ = 0°: cos0° = 1 V_axial = p / (4π…

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Definition: An equipotential surface is a surface on which every point is at the same electric potential. Example: The equatorial plane of a dipole (V = 0 everywhere on it). Properties: 1. No work …

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Relation: E = −ΔV / Δr In words: Electric field at a point = Negative rate of change of potential with distance (negative potential gradient) For uniform field: E = (V_A − V_B) / d Where d = separa…

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Given: • Potential difference V = 12.0 V • Separation d = 3 mm = 3 × 10⁻³ m Formula: E = V / d Step 1: Substitute values E = 12.0 V / (3 × 10⁻³ m) Step 2: Calculate E = 12.0 / 0.003 = 4000 V/m Ans…