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(D) In a uniform electric field, the electric potential $V$ decreases in the direction of the electric field lines. The potential at any point $(x, y)

Vedclass · Accepted Answer

$V_{A}=V_{B}, V_{C} > V_{D}$

Vedclass · Answer

(D) In a uniform electric field, the electric potential $V$ decreases in the direction of the electric field lines. The potential at any point $(x, y)$ in a uniform electric field $\vec{E} = E\hat{i}$ is given by $V = -Ex + 	ext{constant}$.Points on the same vertical line (perpendicular to the field lines) have the same potential because they have the same $x$-coordinate.Looking at the diagram:$1$. Points $A$ and $B$ are at the same vertical position relative to the field lines, but they are not on the same vertical line. However, the question asks for the relationship between potentials. Let's analyze the $x$-coordinates.$2$. Point $C$ is at the leftmost position, so it has the smallest $x$-coordinate, meaning $V_{C}$ is the highest.$3$. Point $D$ is at the rightmost position, so it has the largest $x$-coordinate, meaning $V_{D}$ is the lowest.$4$. Points $A$ and $B$ have the same $x$-coordinate, so $V_{A} = V_{B}$.$5$. Since $C$ is to the left of $D$, $V_{C} > V_{D}$.Thus, the correct relationship is $V_{A} = V_{B}$ and $V_{C} > V_{D}$.

$A$ uniform electric field exists in the plane of the paper as shown. Here $A, B, C$, and $D$ are points on the circle. $V_{A}, V_{B}, V_{C}$, and $V_{D}$ are the potentials at those points respectively. Then:

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