Final answer:
Doubling the potential difference applied across a conductor will double the current density, as per Ohm's law, assuming constant resistance and conductor properties.
Step-by-step explanation:
When the potential difference applied across a given conductor is doubled, the current density will also double. This outcome is consistent with Ohm's law, which states the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R). Therefore, if the voltage is doubled while the resistance remains constant, the current flowing through the conductor will double as well.
Furthermore, the current density (J) is directly proportional to the current and inversely proportional to the cross-sectional area (A) of the conductor as given by the formula J = I/A. Consequently, doubling the current while maintaining the same conductor size will result in the current density doubling. This explains the relationship between voltage, current, and current density within a conductive material.
In essence, a doubled voltage implies a doubled electrical field across the conductor, leading to a doubled current and thus a doubled current density, assuming the conductor's properties do not change with increasing voltage.