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

Answer

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A cylindrical conductor of radius R is shown in the figure, Two thin insulating discs (or dielectric discs) of same radius are placed at the ends of this cylinder. The charges on these discs are $+Q$ and - Q respectively.
An electric field will be created and it is directed from the positive charge $+Q$ towards the negative charge $-Q$.
Due to this electric field, the electrons will be accelerated towards + Q . Such motion continues until the electron neutralizes the charge + Q . This will constitute an electric current.
When this disc is neutralized by the electrons, electrons stop moving. As a result, no current flows. Hence in the considered situation, there will be a current for a short peroid.
Now we can imagine a mechanism where the ends of the cylinder are supplied with fresh charges to make up for any charges neutralized by electrons moving inside the conductor.
In that case, there will be a steady electric field in the conductor. This will result in a continuous current rather than a current for a short period of time.
Electric cells or batteries can maintain a steady electric field that results in a steady current inside the conductor.

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