Monday, 25 February 2019

homework and exercises - Why current density of a point charge satisfies vecJrmdV=qvecv?


I read in a book that if a point charge q at the position x is moving with the velocity v=dx/dt and if the current density generated by the charge is J, then the following relation holds JdV=qv

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 dp/dt=VJ(x,t)dV. Solution: suppose the i-th charge is denoted by qi with the position xi, then p=qixi. the current element generated by every charge is J(x,t)dV=qidxi/dt, so dp/dt=qidxi/dt=VJ(x,t)dV




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