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Electric charge is quantized (q = ne), conserved in isolated systems, and additive, with the elementary unit e = C.
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Coulomb's law gives the force between two point charges as F = kq_{1}q_{2}/ where k = N , and the net force on any charge is the vector sum of all such pairwise forces (superposition).
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The electric field E = kQ/ 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.
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Inside a uniformly charged insulating sphere at radius r < R, the electric field is E = kQr/, which increases linearly from zero at the center to a maximum at the surface.
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For an electric dipole, the axial field is E_axial = 2kp/ and the equatorial field is E_eq = kp/, giving a ratio of 2:1; the potential on the equatorial line is zero.
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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/ (outside) or 0 (inside) for a conducting sphere.
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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.
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Capacitance C = ε_{0}A/d increases by a factor K when a dielectric of constant K is inserted; energy stored is U = ½ = /2C = ½QV.
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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.
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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.
Part of ES-01 — Electrostatics
Electrostatics — 10 Core Sentences
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