Using these, the last equation reads
GEORG SIMON OHM (1787–1854)
Georg Simon Ohm  (1787–
1854) German physicist,
professor at Munich Ohm
was led to his law by an
analogy 
between 
the
conduction of heat: the
electric field is analogous to
the temperature gradient,
and the electric current is
analogous to the heat flow Rationalised 2023-24
Current
Electricity
85
        E l = j r l
or,    E = j r
(3 11)
The above relation for magnitudes E and j can indeed be cast in a
vector  form