<Dd> m e n e d v → e d t = − n e e E → + n e m e ν (v i − v e) − e n e v → e × B →, (\ displaystyle m_ (e) n_ (e) (d (\ vec (v)) _ (e) \ over dt) = - n_ (e) e (\ vec (E)) + n_ (e) m_ (e) \ nu (v_ (i) - v_ (e)) - en_ (e) (\ vec (v)) _ (e) \ times (\ vec (B)),) </Dd> <P> where e (\ displaystyle e), m e (\ displaystyle m_ (e)) and v → e (\ displaystyle (\ vec (v)) _ (e)) are the charge, mass and velocity of the electrons, respectively . Also, ν (\ displaystyle \ nu) is the frequency of collisions of the electrons with ions which have a velocity field v → i (\ displaystyle (\ vec (v)) _ (i)). Since, the electron has a very small mass compared with that of ions, we can ignore the left hand side of the above equation to write </P> <Dl> <Dd> σ (E → + v → × B →) = J →, (\ displaystyle \ sigma ((\ vec (E)) + (\ vec (v)) \ times (\ vec (B))) = (\ vec (J)),) </Dd> </Dl> <Dd> σ (E → + v → × B →) = J →, (\ displaystyle \ sigma ((\ vec (E)) + (\ vec (v)) \ times (\ vec (B))) = (\ vec (J)),) </Dd>

State and explain ohm's law of electricity