Part of ES-01 — Electrostatics

Electrostatics — 10 Core Sentences

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  1. Electric charge is quantized (q = ne), conserved in isolated systems, and additive, with the elementary unit e = 1.6×10191.6 \times 10^{-19} C.

  2. Coulomb's law gives the force between two point charges as F = kq_{1}q_{2}/r2r^{2} where k = 9×1099 \times 10^{9} N m2m^{2} C2C^{-2}, and the net force on any charge is the vector sum of all such pairwise forces (superposition).

  3. The electric field E = kQ/r2r^{2} at a point gives the force per unit positive test charge; its dimensional formula is [MLT^{-3}$$A^{-1}] and it is zero everywhere inside a conductor.

  4. Inside a uniformly charged insulating sphere at radius r < R, the electric field is E = kQr/R3R^{3}, which increases linearly from zero at the center to a maximum at the surface.

  5. For an electric dipole, the axial field is E_axial = 2kp/r3r^{3} and the equatorial field is E_eq = kp/r3r^{3}, giving a ratio of 2:1; the potential on the equatorial line is zero.

  6. Gauss's law states Φ = q_enc/ε_{0} and gives E = λ/2πε_{0}r for an infinite wire, E = σ/2ε_{0} for an infinite plane, and E = kQ/r2r^{2} (outside) or 0 (inside) for a conducting sphere.

  7. Electric potential V = kQ/r is related to field by E = −dV/dr; equipotential surfaces are perpendicular to field lines and no work is done moving a charge along them.

  8. Capacitance C = ε_{0}A/d increases by a factor K when a dielectric of constant K is inserted; energy stored is U = ½CV2CV^{2} = Q2Q^{2}/2C = ½QV.

  9. When a dielectric is inserted with the battery connected, V is constant and energy increases by K; when disconnected, Q is constant and energy decreases by K.

  10. In series capacitor combinations, charge is the same on all and the smallest capacitor stores the most energy; in parallel combinations, voltage is the same and the largest capacitor stores the most energy.

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