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1.3. Electromagnetic Mass.

1.3.1. Charge/Field Electromagnetic Momentum.

The quantity S/c² (where S is the Poynting vector) has the dimensions of momentum per unit volume. And it is readily shown that the total momentum, in the electromagnetic field of a spherical shell of charge whose velocity is constant, is q²v/6pe_oRc² where R is the shell’s radius. This suggests that an "electromagnetic mass" be assigned to the charge/field:

. (1.3.1_1)

Note that m_elecmag is inversely proportional to R. Thus a finite point charge (with zero R) has infinite electromagnetic mass!

1.3.2. Spherical Shell with Constant Velocity.

Since the interactive forces among all the constituent point charges comprising a spherical shell sum to zero when v is constant, the agent counteractions sum to zero. This zero force translates to zero impulse over any interval of time, and the momentum in the field accordingly remains a constant m_elecmagv.

1.3.3. Spherical Shell with Constant a.

If a is constant, then the driving agent must exert a constant inertial force component in the same direction as a. A computer program indicates that this force does indeed equal m_elecmaga. If this force is parallel to v (the shell’s velocity) then the agent does positive or negative work on the charge/field in any given time interval. In the positive case the momentum in the field increases with time; momentum (and energy) flows from the agent out into the field. In the negative case the field momentum decreases with time; momentum flows in from the field to the agent. In general, when a is constant, the law of motion is

. (1.3.3_1)

1.3.4. Spherical Shell with Nonzero da/dt.

As previously pointed out, in the case of a distribution of charge there is also a net reactive force component when da/dt is nonzero. And the driving agent must counteract the net da/dt-induced "radiation reaction" component of the total reactive force (as well as any nonzero a-induced or inertial reaction components) in order to maintain the distribution’s shape. In the case of spherical shells of charge, the da/dt-induced "radiation reaction" force is independent of the shell radius:

. (1.3.4_1)

The part of the total agent force, expended to counteract this radiation part of the net reaction force, is

. (1.3.4_2)

Note that whenever F_radiative and v point in the same direction, then their dot product is positive and the agent is expending power. A computer program (Reference Appendix 1.3.4_1) indicates that, in the case of periodic motion, the power expended per cycle by F_radiative equals the electromagnetic energy flux per cycle out through an enclosing surface.