Single-Particle Electrodynamics - Assassination Science

point of the loop at angle θ to the x-axis is then given by
z(θ) = ε { i cos θ + j sin θ } . (4.22)
Clearly, the direction of the magnetic moment µ of the current loop will lie
along the z-axis. We choose to make it point in the positive z-direction:
µ ≡ µk. (4.23)
This then requires the (Engineer’s) electric current I in the loop to flow in
the direction of positive θ, i.e., counter-clockwise as viewed from a position
“above” the loop (z > 0). The definition of the magnitude µ of a planar
electric-current magnetic dipole is simply the product of the area of the loop
by the Engineer’s current I flowing around it [113]; in our case,
µ ≡ πε 2 I. (4.24)
Now, we are here forming the Engineer’s current I from equal and opposite
lineal streams of positive and negative charge, around the loop: the charge
densities cancel, and their current densities add. Thus, half of I will be due
to the integral of the qv contributions of the positive charges, and half will
be due to the same integral of the contributions of the negative charges. We
denote the total number of positive charges circulating in the loop as n; the
number of negative charges circulating in the loop is thus also n. The number
of charges n will be taken to infinity at the end of the calculations, and the
product of the other quantities taken to zero to compensate, to provide a
“continuous” stream of charge. Each individual positive or negative charge
is denoted +q or −q respectively. We denote the speed of each charge in its
“orbital” motion around the loop by v orb . The Engineer’s current I is then
simply given by
I = 2 nqv orb
2πε , (4.25)
where the factor 2 outside the front is due to the presence of both positive
and negative charges in circulation; the factor 2πε is the circumference of the
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