I read in a book that if a point charge q at the position →x is moving with the velocity →v=d→x/dt and if the current density generated by the charge is →J, then the following relation holds →JdV=q→v
why is it like this?
PS: it is from an exercise: if the electric dipole of a system consisting of electric charges is →p, prove d→p/dt=∫V→J(→x,t)dV. Solution: suppose the i-th charge is denoted by qi with the position →xi, then →p=∑qi→xi. the current element generated by every charge is →J(→x,t)dV=qid→xi/dt, so d→p/dt=∑qid→xi/dt=∫V→J(→x,t)dV
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