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EMISSION OF RADIATION FROM AN ACCELERATED CHARGED PARTICLE
REACHING THE SPEED OF LIGHT c, AS THE ULTIMATE LIMIT, WITH CONSTANT MASS m
VELOCITY OF TRANSMISSION OF FORCE RELATIVE TO A PARTICLE MOVING AT VELOCITY v, is c - v
TOTAL ENERGY CONTENT E IS
E = 1/2m(c2 + v2) i
THE ELECTRODYNAMIC FIELD OF A CHARGE MOVING AT TIME t WITH ACCELERATION dv/dt ACTS ON THE CHARGE TO PRODUCE THE INERTIAL FORCE EQUAL TO -m(dv/dt)
THE ACCELERATING FORCE F ON A PARTICLE OF CHARGE q AND MASS m MOVING AT TIME t WITH VELOCITY v AND ACCELERATION dv/dt IN AN ELECTROSTATIC FIELD OF MAGNITUDE E, IS GIVEN, IN ACCORDANCE WITH NEWTON'S SECOND LAW OF MOTION, BY VECTOR EQUATION:
F = qE/c(c - v) = m(dv/dt) ii
FOR A PARTICLE MOVING IN THE DIRECTION OF THE ACCELERATING FIELD, THE SCALAR EQUATION IS:
F = qE(1 - v/c) = m(dv/dt) iii
FOR A PARTICLE MOVING AGAINST THE FIELD, THE EQUATION IS:
F = qE(1 + v/c) = -m(dv/dt) iv
RADIATION REACTION FORCE R IS:
R = F - qE = qE/c(c - v) - qE v
RADIATION POWER P IS PRODUCT
P = - R . v vi
