# Direction of current in concentric cylinders

Example 7.2 in David Griffiths E & M book (3rd edition) has a side view of 2 concentric cylinders, with smaller radius $a$ and larger radius $b$. The region in between $a$ and $b$ has conductivity $\sigma$. "If they are maintained at a potential difference $\textit{V}$, what current flows from one cylinder to the other for a given length $L$?"

The E field is pointing radially outward along $\textit{s}$. My question is: what direction is the current? Do electrons flow in the opposite direction of an E field? If so, does that mean the current is flowing radially inward, along $\textit{-s}$, from $b$ to $a$?

## 2 Answers

Yes - electrons flow from the negative to the positive, so in the opposite direction to the conventional direction of the electric field (which points from positive to negative). So if the E field points outwards, the electrons flow from the outer to the inner cylinder.

The direction does not affect the answer (the calculation of the flow) though - at least not in magnitude. And while you might say the electrons flow from outer to inner, you would still say that the current (conventional sense) flows from inner to outer.

The Lorentz force on a charge in an electromagnetic field is $$F=q(E+v \times B) \ \ .$$ For an electron between the cylinders, $q$ is negative, and $E$ is defined as pointing outward, so the electron will experience a force radially inward. But due to the unfortunate sign convention used for currents, electrons flowing inward means that the conventional current is flowing radially outward.