Electrostatics and Capacitors
What this domain tests
Electrostatics and Capacitors covers Coulomb forces, electric field and potential, Gauss's law, conductors, dielectrics and capacitor networks. CHSE questions often combine field-line reasoning with capacitor energy and sharing.
Core rules
- Coulomb force between point charges: F = kq1q2/r², k = 9×10⁹ N m² C⁻²; force is a vector along the line joining charges.
- Electric field E = F/q0; potential V = W/q0; E = −dV/dr.
- Gauss's law: Φ = q_enclosed/ε0. Use symmetry: sphere, infinite line, infinite sheet.
- Capacitance C = Q/V; parallel plate C = ε0A/d, with dielectric C = Kε0A/d.
- Series: 1/C = Σ1/Ci; parallel: C = ΣCi. Energy U = ½CV² = Q²/2C.
Worked example
A 2 μF capacitor charged to 100 V is joined to an uncharged 3 μF capacitor. Initial charge Q = CV = 200 μC. Common potential V′ = Q/(C1+C2) = 200 μC/5 μF = 40 V. Initial energy = ½(2 μF)(100 V)² = 0.010 J; final = ½(5 μF)(40 V)² = 0.004 J. Energy lost = 0.006 J, appearing as heat and radiation in the connecting wires.
Traps
- Mixing up series and parallel formulas for capacitors; they are opposite to resistors.
- Forgetting that a dielectric reduces field and increases C, while battery connected or disconnected decides whether V or Q is fixed.
- Treating potential as a vector, or dropping the sign of charge.