Electrostatics: MDCAT Notes and MCQs
Coulomb's law
- F = k q1q2/r², k = 1/4πε0 = 9 × 109 N m² C−2; ε0 = 8.85 × 10−12 C² N−1 m−2.
- In a medium of relative permittivity (dielectric constant) εr: Fmed = Fvac/εr — always smaller (εr of water ≈ 80, air ≈ 1.0006).
Electric field
- Region around a charge where another charge feels a force. E = F/q0 (N C−1 = V m−1), direction = force on a positive test charge.
- Point charge: E = kq/r², radially outward for +q, inward for −q.
- Two charges: add field vectors. Midpoint of equal like charges: E = 0 (neutral point). Midpoint of equal opposite charges: fields add, E = 2kq/(d/2)² = 8kq/d², directed towards the negative charge.
- Field lines: start on +, end on −; never cross; closer lines = stronger field. Opposite charges: lines connect (dipole). Like charges: lines repel, neutral point between them.
- Infinite sheet of charge (density σ): E = σ/2ε0, uniform, perpendicular to the sheet (away for +, towards for −). Near a charged conducting plate / between two oppositely charged parallel plates: E = σ/ε0, uniform.
Electric potential
- Potential at a point = work done in bringing a unit positive charge from infinity to that point: V = W/q0. Scalar.
- Unit volt = 1 J C−1: potential is 1 V if 1 J of work is done to bring +1 C from infinity.
- Point charge: V = kq/r (derived by integrating work against E = kq/r² from ∞ to r). Potential energy U = qV = kq1q2/r.
- E = −ΔV/Δr (potential gradient). 1 eV = 1.6 × 10−19 J.
Capacitor charging & discharging (RC circuit)
- C = Q/V (farad). Parallel-plate: C = ε0εrA/d.
- Charging: q = q0(1 − e−t/RC) — charge rises exponentially; current decreases.
- Discharging: q = q0e−t/RC.
- Time constant τ = RC (seconds): time to charge to 63% of final charge, or discharge to 37%. Larger RC → slower. Used in timers, flashing lights, wipers.
PMDC learning outcomes for this unit
- Coulomb's law, field, potential, capacitors: 8.1 State Coulomb's law and explain that force between two point charges is reduced in a medium other than free space
- Coulomb's law, field, potential, capacitors: 8.2 Describe the concept of an electric field as an example of a field of force
- Coulomb's law, field, potential, capacitors: 8.3 Calculate magnitude and direction of the electric field at a point due to two charges with same or opposite signs
- Coulomb's law, field, potential, capacitors: 8.4 Sketch electric field lines for two point charges of equal magnitude with same or opposite signs
- Coulomb's law, field, potential, capacitors: 8.5 Describe and draw the electric field due to an infinite conducting plate of positive or negative charge
- Coulomb's law, field, potential, capacitors: 8.6 Define electric potential at a point in terms of work done in bringing unit positive charge from infinity to that point
- Coulomb's law, field, potential, capacitors: 8.7 Define the unit of potential
- Coulomb's law, field, potential, capacitors: 8.8 Derive an expression for electric potential at a point due to a point charge
- Coulomb's law, field, potential, capacitors: 8.9 Demonstrate charging and discharging of a capacitor through a resistance