Two equal positive charges are kept at points A and B. The electric potential at the points between

Question

Two equal positive charges are kept at points A and B. The electric potential at the points between A and B (excluding these points) is studied while moving from A to B. The potential

Professor PC Thomas Classes · Answer

- Near Point A: When you are very close to point A , the distance $r_A$ is tiny, so $V_A$ is extremely large (approaching $+\infty$ ). The distance $r_B$ is large, so $V_B$ is a smaller, finite positive value. Their sum, $V_{	ext {total }}$, is therefore extremely large.
- Near Point B: When you are very close to point B, the situation is reversed. $r_B$ is tiny, so $V_B$ is extremely large (approaching $+\infty$ ). $r_A$ is large, so $V_A$ is a smaller, finite positive value. Their sum, $V_{	ext {total }}$, is again extremely large.
- At the Midpoint: Exactly in the middle, you are equidistant from both charges $\left(r_A=ight. \left.r_Bight)$. The potential is $V_{	ext {total }}=k \cdot \frac{q}{r_A}+k \cdot \frac{q}{r_B}$, which is a finite positive value. By symmetry, this is the point where the potential will be at its lowest.
The potential starts infinitely high (just after A), decreases as you move toward the center, reaches a minimum value at the midpoint, and then increases again as you approach point $B$ (where it goes back to infinity).