Question

assume that two of the electrons at the negative terminal have attached themselves to a nearby neutral atom. there is now a negative ion with a charge - 2e at this terminal. what are the electric potential and electric potential energy of the negative ion relative to the electron? the electric potential and the electric potential energy are both twice as much. the electric potential is twice as much and the electric potential energy is the same. the electric potential is the same and the electric potential energy is twice as much. the electric potential and the electric potential energy are both the same. the electric potential is the same and the electric potential energy is increased by the mass ratio of the oxygen ion to the electron. the electric potential is twice as much and the electric potential energy is increased by the mass ratio of the oxygen ion to the electron.

Explanation:

Step1: Recall electric - potential definition

Electric potential $V$ at a point in an electric field is a property of the field and is independent of the charge placed at that point. So, the electric potential at the negative - terminal is the same regardless of whether a single electron or a negative ion with charge $- 2e$ is present there.

Step2: Recall electric - potential energy formula

The electric potential energy $U$ of a charge $q$ in an electric potential $V$ is given by $U = qV$. If the charge of the particle changes from $-e$ (for an electron) to $-2e$ (for the negative ion) and $V$ is constant, then $U_{ion}=(-2e)V$ and $U_{electron}=(-e)V$. So, $U_{ion} = 2U_{electron}$.

Answer:

The electric potential is the same and the electric potential energy is twice as much.