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 desired acceleration. Referring again to fig. 1, since the body is being accelerated in the Y direction, its total velocity and hence its mass are increasing. This increasing mass is accompanied by increasing momentum in the X direction even when the velocity in that direction remains constant. The component force $$\mathsf{F}_{x}$$ is necessary for the production of this increase in X-momentum.

In predicting the path of moving electrons with the help of the fifth equation of electromagnetic theory, $$\mathsf{F}=\mathsf{E}+\frac{1}{c}\mathsf{v}\times\mathsf{H},$$, we find an interesting application of equation (5).

Application in Electromagnetic Theory.

Consider a charge $$\epsilon$$ constrained to move in the X direction with the velocity $$v$$ and let it be the origin of a system of moving coordinates Y$$\epsilon$$X (fig. 2). Suppose now a test electron $$t$$, of unit charge, situated at the point $$x=0$$, $$y=y$$,



moving in the X direction with the same velocity $$v$$ as the charge $$\epsilon$$, and also having a component velocity in the Y direction $$u_y$$. Let us predict the nature of its motion under the influence of the charge $$\epsilon$$.

The moving charge $$\epsilon$$ will be surrounded by electric and magnetic fields whose intensities at any point are given by the following expressions, obtained by integrating Maxwell’s