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Unformatted text preview: Chapter 2 Electricity & Magnetism
2.1 The Maxwell equations
The classical electromagnetic ﬁeld can be described by the Maxwell equations. Those can be written both as differential and integral equations: (D · n )d2 A = Qfree,included (B · n )d2 A = 0 E · ds = − dΦ dt dΨ dt (B · n )d2 A. np2 0 3ε0 kT · D = ρfree ·B =0 ×E =− ∂B ∂t ∂D ∂t H · ds = Ifree,included + For the ﬂuxes holds: Ψ = (D · n )d2 A, Φ = × H = Jfree + The electric displacement D, polarization P and electric ﬁeld strength E depend on each other according to: D = ε0 E + P = ε0 εr E , P = p0 /Vol, εr = 1 + χe , with χe = The magnetic ﬁeld strength H , the magnetization M and the magnetic ﬂux density B depend on each other according to: B = µ0 (H + M ) = µ0 µr H , M = m/Vol, µr = 1 + χm , with χm = µ0 nm2 0 3kT 2.2 Force and potential
The force and the electric ﬁeld between 2 point charges are given by: F12 = Q1 Q2 F er ; E = 4πε0 εr r2 Q The Lorentzforce is the force which is felt by a charged particle that moves through a magnetic ﬁeld. The origin of this force is a relativistic transformation of the Coulomb force: FL = Q(v × B ) = l(I × B ). The magnetic ﬁeld in point P which results from an electric current is given by the law of Biot-Savart, also known as the law of Laplace. In here, d l I and r points from d l to P : dBP = µ0 I dl × er 4π r 2 If the current is time-dependent one has to take retardation into account: the substitution I (t) → I (t − r/c) has to be applied.
2 The potentials are given by: V 12 = − 1 E · ds and A = 1 B × r . 2 ...
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.
- Spring '10