Overview
This lecture is a brief revision of all the main topics in the "Electric Potential and Capacitance" chapter, including definitions, formulas, derivations, and important points.
Electric Potential and Potential Difference
- Electric Potential: Work done to bring a unit charge from infinity to a point.
- Potential Difference: Work done to bring a unit charge between two points; Delta V = work done / charge.
- Formula: V = KQ/r (for a point charge), V is a scalar quantity.
Potential Due to Point Charge and Dipole
- For point charge V = KQ/r.
- For dipole at axial point: V = KP/(r^2 - a^2), where P = q×2a.
- For dipole at equatorial point: V = 0.
Equi-potential Surfaces
- A surface where potential is the same everywhere.
- Equi-potential surfaces never intersect.
- Work done between them is zero; where they are close, electric field is stronger.
Relation Between Electric Field and Potential
- E = -dV/dr; electric field is the negative of the potential gradient.
- Potential gradient: dV/dr.
Potential of Spherical Shell
- Inside the shell electric field = 0; hence, potential is constant.
- On surface or inside: V = KQ/R; outside: V = KQ/r (r>R).
Electric Potential Energy
- Definition: Work done to assemble or separate a system of two charges is called electric potential energy.
- For two charges: U = KQ ₁Q₂/r.
- For three charge system: use the above formula for each pair.
Potential Energy of Dipole
- In uniform electric field: U = -pEcosθ.
- If two angles are given: U = -pE(cosθ₂ - cosθ₁).
Capacitance and Capacitor
- Capacitor is a device that stores energy.
- Q ∝ V, Q = CV, where C = capacitance, C = Q/V.
- Spherical capacitor C = 4πε₀R.
- Capacitance depends on size and medium.
Parallel Plate Capacitor
- Formula: C = Aε₀/d, where A = area, d = distance between plates.
- Dielectric slab (thickness T, dielectric constant K) formula: C = Aε₀ / [d-T + (T/K)].
- Fully filled: C = Kε₀A/d.
- For conducting slab: take k = ∞.
Capacitors in Series and Parallel
- In series: 1/C_net = 1/C₁ + 1/C₂ + …
- In parallel: C_net = C₁ + C₂ + …
Energy Stored in Capacitor
- Energy = (1/2)CV² = (1/2)Q²/C = (1/2)QV.
Dielectrics and Their Types
- Dielectric: a type of insulator that does not allow charge flow.
- Two types: Polar (e.g., HCl), Non-polar (e.g., O₂, CO₂).
- Without electric field dipole moment is zero in both; under electric field polar has non-zero net moment.
Key Terms & Definitions
- Electric Potential (V) — Work done to bring a unit charge from infinity to a point.
- Potential Difference (ΔV) — Work done to bring a unit charge between two points.
- Capacitance (C) — The ability of a capacitor to store charge.
- Dielectric — A type of insulator that does not allow charge flow.
- Electric Field (E) — Negative of the potential gradient, E = -dV/dr.
Action Items / Next Steps
- Memorize formulas for potential and capacitance.
- Remember types of dielectrics and their examples.
- Solve problems on series and parallel capacitors.
- Practice exercise questions.