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    Maxwell: THE Equations

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    Eddie
    1. This document discusses Maxwell's equations and the conservation of momentum in electrodynamics. 2. It shows that the change in mechanical momentum over time equals the external force minus the flow of momentum through a surface due to the Maxwell stress tensor. 3. The total momentum, which is the sum of the mechanical and field momentum, is conserved according to this analysis.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Maxwell: THE Equations

    Uploaded by

    Eddie
    9 views1 page
    1. This document discusses Maxwell's equations and the conservation of momentum in electrodynamics. 2. It shows that the change in mechanical momentum over time equals the external force minus the flow of momentum through a surface due to the Maxwell stress tensor. 3. The total momentum, which is the sum of the mechanical and field momentum, is conserved according to this analysis.

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    rte

    Original Title

    166

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    1. This document discusses Maxwell's equations and the conservation of momentum in electrodynamics. 2. It shows that the change in mechanical momentum over time equals the external force minus the flow of momentum through a surface due to the Maxwell stress tensor. 3. The total momentum, which is the sum of the mechanical and field momentum, is conserved according to this analysis.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views1 page

    Maxwell: THE Equations

    Uploaded by

    Eddie
    1. This document discusses Maxwell's equations and the conservation of momentum in electrodynamics. 2. It shows that the change in mechanical momentum over time equals the external force minus the flow of momentum through a surface due to the Maxwell stress tensor. 3. The total momentum, which is the sum of the mechanical and field momentum, is conserved according to this analysis.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 1

    166 CHAPTER 7.

    THE MAXWELL EQUATIONS

    for the charged particle, i.e.

    d (mechanical momentum)
    = external force
    dt

    =/[EV.D+(VxH-- > 1
    at x B dV

    + J [EV D + H
    0
    v +(V x H) x B + (V x E) x D]dV.
    +_ _8B
    at

    It can be shown that the remaining terms can be combined in the following
    way:

    d(mechanica1 momentum)
    dt
    } = -: /(D x B)jdv +J K
    a ZjW
    j

    where
    1
    Tij = (DiEj + B i H j ) - Sij-(D * E + B . H).
    2
    This expression is equal to Tji for D = E E , B= p H . The expression Tij is
    called Maxwell stress tensor. In a self-evident way we have (on application
    of Gauss divergence theorem)

    d
    -(pmech
    dt
    + pfield ) j - JF T,j(dF)i = 0. (7.29)

    The term on the right represents the flow of momentum through the surface
    F . If this surface is shifted to infinity, so that the term on the right is zero,
    we have
    P +
    pfield = constant,

    where Pfield = J d V p f i e l d , pfield = D x B = volume density of the field


    momentum Pfield. This is the law of conservation of m o m e n t u m in elec-
    trodynamics. Note that the field momentum density is not given by the
    Poynting vector! The expression

    Kj = T,j(dF)i

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