# Maxwell's Characteristics: The Basic Laws Of Hydrodynamics

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Chapter 1 INTRODUCTION

The study of magnetohydrodynamics (MHD) draws from two well known branches of physics, electrodynamics and hydrodynamics.The basic laws of electrodynamics described in the form of Maxwell’s Equations where The hydrodynamics of a fluid is expressed in the form of conservation laws of mass, momentum and energy.The magnetohydrodynamic phenomena are a consequence of the mutual interaction of the fluid flow and the magnetic field. As is well known, a conductor crossing magnetic field lines gives rise to an induced electric field, which causes an electric current in the conducting fluid.
The following are the Maxwell,s equations
∇⋅D = ρcf ∇⋅B = 0
∇×E = −∂B
∂t
∇×H = J f + ∂D
∂t
(2) MACROSCOPIC (LOW FREQUENCY, LONG WAVELENGTH) BEHAVIOR. (3) ASSUME THAT THE GYRORADIUS IS SMALL.
(4) ASSUME THE PLASMA IS FULLY IONIZED.
(5) LIMITED APPLICABILITY TO WEAKLY IONIZED PLASMAS LIKE THE PHOTOSPHERE AND CHROMOSPHERE.
(6) ASSUME COLLISIONS ARE FREQUENT ENOUGH THAT THE PARTICLE DISTRIBUTION FUNCTION IS MAXWELLIAN.
1.3 THE IDEAL MHD
An ideal conducting fluid is one with infinite conductivity σ, or zero electrical resistivity η, and zero viscosity coefficients µ and ξ.In the ideal MHD approximation we regard the fluid as a perfect electrical conductor.Ideal MHD assumes no resistivity, viscosity, thermal conduction, or radiative cooling.This is a highly idealized situation, not attainable in nature; it is called ideal MHD. However, it turns out that ideal MHD describes dynamical properties of hot, strongly magnetized plasmas. This is because most hot plasmas are excellent (although not perfect) conductors of electricity.
1.31 IDEAL MHD EQUATIONS

CONTINUITY EQUATION AMPERE’S LAW J B FARADAY’S LAW C∇ × E IDEAL OHM’S LAW E + V×C B = 0

1.4 RESISTIVE

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