• # question_answer A point charge Q is placed at point O as shown in figure. Is the potential difference ${{V}_{A}}-{{V}_{B}}$ positive, negative or zero, if Q is (i) positive, (ii) negative?

${{V}_{A}}-{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{OA}-\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{OB}=\frac{Q}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{OA}-\frac{1}{OB} \right]$ From the diagram the distance OA < OB. $\therefore \frac{1}{OA}-\frac{1}{OB}$ is positive.
 (i) If Q is positive, then ${{V}_{A}}-{{V}_{B}}$ is positive. (ii) If 0 is negative, then  ${{V}_{A}}-{{V}_{B}}$ is negative.