Explain the current formed in solid conductors in the presence of an external electric field.

(N/A) Consider a metallic cylinder of radius $R$ as shown in the figure.
We consider two thin circular discs which have $+Q$ and $-Q$ charges distributed over them. If we attach these two discs to the two flat surfaces of the cylinder,an electric field $E$ is established,and a current is produced which is directed from the positive to the negative charge.
Due to this electric field in the cylinder,electrons will be accelerated toward the $+Q$ charge.
These electrons,as long as they are moving,will constitute an electric current. In this condition,the current will be formed for a very short time and will then stop as the charges are neutralized.
If we consider a mechanism like a cell or a battery,in which the amount of charge $+Q$ that is neutralized is continuously replenished by an equal amount of $-Q$ charge at the other end,then a steady electric current can be maintained.