Chapter 2Electricity & Magnetism2.1The Maxwell equationsThe classical electromagnetic field can be described by theMaxwell equations. Those can be written both asdifferential and integral equations:(D·n)d2A=Qfree,included∇·D=ρfree(B·n)d2A= 0∇·B= 0E·ds=-dΦdt∇ ×E=-∂B∂tH·ds=Ifree,included+dΨdt∇ ×H=Jfree+∂D∂tFor the fluxes holds:Ψ=(D·n)d2A,Φ=(B·n)d2A.The electric displacementD, polarizationPand electric field strengthEdepend on each other according to:D=ε0E+P=ε0εrE,P=∑p0/Vol,εr= 1 +χe, withχe=np203ε0kTThe magnetic field strengthH, the magnetizationMand the magnetic flux densityBdepend on each otheraccording to:B=μ0(H+M) =μ0μrH,M=∑m/Vol,μr= 1 +χm, withχm=μ0nm203kT2.2Force and potentialThe force and the electric field between 2 point charges are given by:F12=Q1Q24πε0εrr2er;E=FQThe Lorentzforce is the force which is felt by a charged particle that moves through a magnetic field. The
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Magnetic Field, Electric charge, Classical Electromagnetic Field, dt dΨ dt