# Calculating the electric and magnetic field between two hollow cylinders

I am given the following question:

Two long coaxial cylindrical conductors of radii $a$ and $b$ ($b$ < $a$) are thin and hollow. There is a vacuum between the conductors ($b$ < $r$ < $a$, where r is the radial distance from the axis). The conductors are maintained at a potential difference $V$$0$ and carry equal but opposing currents of magnitude $I$ (in the direction of the axis of the cylinders). Find the magnitude and direction of the electric and magnetic fields in the region between the conductors, defining carefully the direction of the currents and the sign of the potential difference you have assumed.

From what I know, there's a magnetic field present between the two cylinders, which is produced by the current passing through the inner cylinder (all I need to do is to use Ampere's law). Current in the outer cylinder doesn't affect the magnetic field between them. However, how can there be an electric field present?

Clearly, magnetic field occurs only between the two cylinders just like as a current carrying wire, and the electic field occurs also in the region due to potential difference $V_0$. For a steady state current the electric field only exists along the direction of current.