Pick an origin and assume that the body is made up of n point masses m i at positions described by the vectors r i i 1. Tensor which depends on two directions one normal to the area and other that of the force on it. The quantity sis the maxwell stress tensor for magnetostatic. Meaning of the maxwell tensor 4 charges reside at the surface of a conductor. How can we identify the components of the magnetic field, which is a pseudovector, with any of the components of a proper4 tensor.
Electromagnetic potentials making use of the homogeneous maxwell equations we want to introduce the electromagnetic potentials. Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity, electromagnetic theory and many other disciplines of science and engineering. Pdf electromagnetic force and the maxwell stress tensor in. In electromagnetism, the electromagnetic tensor or electromagnetic field tensor sometimes called the field strength tensor, faraday tensor or maxwell bivector is a mathematical object that describes the electromagnetic field in spacetime. Key words relativity, electrodynamics, maxwells equations, minkowski, premetric electrodynamics, energymomentum tensor. Since the average of cos2 xover a single cycle is 1 2, the average momentum. For example, a point charge at rest gives an electric field. Pdf symmetric energymomentum tensor in maxwell, yang. Theory and applications of the maxwell stress tensor field precision. It holds for all conceivable systems and is subject only to the validity of local equilibrium a constraint in frequency but not in the type and strength of. The electromagnetic field tensor let us now investigate whether we can write the components of the electric and magnetic fields as the components of some proper 4tensor.
The reader must be prepared to do some mathematics and to think. The transformation of electric and magnetic fields under a lorentz boost we established even before einstein developed the theory of relativity. Introduction to tensor calculus for general relativity. The method is seldom discussed in introductory texts on. Mit opencourseware for any use or distribution of this. But avoid asking for help, clarification, or responding to other answers. This is obtained from the basic contravariant field strength tensor by the substitutions. Maxwell stress tensor and electromagnetic waves 2 thus there is no momentum. How are maxwells equations stated in the language of tensors.
How can we identify the components of the magnetic field, which is a pseudovector, with any of the components of a proper4tensor. Maxwell tensor is reputed to provide magnetic forces, and. An introduction to tensors for students of physics and. The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism in particular, maxwells equations and the lorentz force in a form that is manifestly invariant under lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. The maxwell stress tensor may be used to calculate electric and magnetic forces on objects. Currents and the energymomentum tensor in classical field.
In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on. The volume integral vanishes and the surface integral. The electromagnetic field tensor let us now investigate whether we can write the components of the electric and magnetic fields as the components of some proper 4 tensor. In undergraduate physics you learned that this was. Construction of the stressenergy tensor we may build the stressenergy tensor by considering. Currents and the energymomentum tensor in classical field theory. The maxwell stress tensor named after james clerk maxwell is a symmetric secondorder tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. Tensor eletromagnetico wikipedia, a enciclopedia livre. To check on this, recall for point charges we had ji ae av i a t 3r r at.
Maxwells stress tensor t let us use the lorentz force law to calculate the total electromagnetic force em fttot due to the totality of the electric charges contained within a source volumev. We know that efields can transform into bfields and vice versa. A basic knowledge of vectors, matrices, and physics is assumed. The maxwell stress tensor is a symmetric secondorder tensor used in classical. Maxwells equations are the fundamental equations of classical electromagnetism and electrodynamics. This is because they are written in the language of 3. Shapiro maxwells theory of electromagnetism can be expressed in terms of a 4vector. However, the maxwell equations as they stand, written in the form given in equation 1. We now have learned the transformation properties of th electric and magnetic fields and together they form an. While the electromagnetic force is microscopically simply the lorentz force, its macroscopic form is more complicated, and given by expressions such as the maxwell stress tensor and the kelvin force.
Maxwell s theory of electromagnetism into special relativity. Deriving maxwells equations from electromagnetic tensor. Maxwell equations in lorentz covariant integral form scielo. We find it useful to define the maxwell stress tensor. Closely associated with tensor calculus is the indicial or index notation. Calculation of the maxwell stress tensor and the poisson. Maxwells theory of electromagnetism into special relativity.
Pdf purpose the purpose of this paper is to clarify the status of maxwells tensor. Pdf electromagnetic force and the maxwell stress tensor. It follows at once that scalars are tensors of rank 0,0, vectors are tensors of rank 1,0 and oneforms are tensors of. We need only to calculate at most six components because the stress tensor is symmetric. There are three reasons why equation 11 is better suited to a numerical calculation than equation 2. Maxwells equations for electromagnetic theory have. One way to see this is to make the charge layer a finite. They can be stated in integral form, in differential form a set of partial differential equations, and in tensor form. Shapiro maxwell s theory of electromagnetism can be expressed in terms of a 4vector. A semiintuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and similar higherorder vector products. In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the lorentz force law. The maxwell stress tensor given in terms of thermodynamic variables, the maxwell tensor is an unequivocally macroscopic, coarsegrained quantity.
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