When is the potential difference between two points defined as one volt?

The potential difference between two points is defined as one volt when one joule of work is done moving one coulomb of charge from one point to another. This definition establishes a clear relationship between work (energy) and electric charge in the context of electric potential.

To unpack this, the unit of potential difference, the volt (V), is derived from the formula for electric potential difference, which is given by the equation:

[ V = \frac{W}{Q} ]

where ( V ) is the potential difference in volts, ( W ) is the work done (in joules), and ( Q ) is the charge (in coulombs). If we set ( W ) to 1 joule and ( Q ) to 1 coulomb, we find that ( V = \frac{1 , \text{J}}{1 , \text{C}} = 1 , \text{V} ). This precise relationship encapsulates the concept of electric potential in a straightforward way.

In considering the other options, moving two coulombs of charge would yield 0.5 volts of potential difference for one joule of work done, which does not meet the definition for one volt.