Work by electric field depends only on potential difference between endpoints Steps: - In a uniform electric field, the work done on a charge is $W = q \Delta V$, where $\Delta V$ is the potential difference between start and end points. - Potential difference $\Delta V = - \vec{E} \cdot \Delta \vec{r}$, so it depends only on the displacement component parallel to the field. - For paths P to S and Q to R, these connect points with the same vertical (field-direction) displacement, yielding identical $\Delta V$. - Other path pairs have different displacements along the field, resulting in different $\Delta V$. Why C is correct: - Paths P to S and Q to R span the same change in electric potential, as per the conservative nature of electrostatic fields ($W = q \int \vec{E} \cdot d\vec{l}$, path-independent). Why the others are wrong: - A: P to R and Q to S have unequal field-parallel displacements. - B: P to Q and R to S are likely …