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1st lecture The Maxwell equations

# 1st lecture The Maxwell equations - 1st lecture The Maxwell...

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1 st lecture The Maxwell equations There are four basic equations, called Maxwell equations, which form the axioms of electrodynamics. The so called local forms of these equations are the following: rot H = j + D / t (1) rot E = - B / t (2) div B = 0 (3) div D = ρ (4) Here rot (or curl in English literature) is the so called vortex density, H is vector of the magnetic field strength, j is the current density vector, D / t is the time derivative of the electric displacement vector D , E is the electric field strength, B / t is the time derivative of the magnetic induction vector B , div is the so called source density and ρ is the charge density. While the above local or differential forms are easy to remember and useful in applications, they are not so easy to understand as they use vector calculus to give spatial derivatives of vector fields like rot H or div D . The global or integral forms of the Maxwell equations are somewhat more complicated but at the same time they can be understood without knowing vector calculus. They are using path, surface, and volume integrals, however: G H dr = I + I DISP (1) G E dr = - ∂Φ B / t (2) A B dA = 0 (3) A D dA = V ρ dV (4) where I is the electric current I = A j dA , I DISP is the so called displacement I DISP = A ( D /

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1st lecture The Maxwell equations - 1st lecture The Maxwell...

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