# How does electrical current have energy? (when electrons move very slowly through circuit)?

How does electrical current have energy? (when electrons move very slowly through circiut )

In an electrical circuit, an electrical current $I$ in a conductor with resistance $R$ produces an energy per time (as heat) $$W=I V=R I^2$$ This energy corresponds to the energy gained from the electric field by each charge carrier (electron) when traversing the potential difference (voltage) over the resistance $R$ $$I=Q/t=ne/t$$ Thus $$W=neV/t$$ On the other hand, a stationary electric current $I$ produces a magnetic field $B$ around it which has the magnetic field energy density $$u=\frac {B^2}{2\mu_0}$$ The work corresponding to this total magnetic field energy has to be done in order to set up the stationary current. This is related to the phenomenon of self-induction.